Rice-Wheat System Spatial Multivariate Modeling Approach

1 Introduction

#rm(list = ls())
if (!require("pacman")) install.packages("pacman")
pacman::p_load(sp, mgcv, bamlss,BayesX,R2BayesX,sf,spdep,rio,distreg.vis)

setwd("C:/Users/MMKONDIWA/OneDrive - CIMMYT/Documents/GitHub/Rice_Wheat_System_SDS_Tool")
# Multivariate geoadditive model
# remotes::install_git("https://git.uibk.ac.at/c4031039/mvnchol")
#
library(sp)
library (mgcv)
library(mvnchol)
library(BayesX)
library(R2BayesX)
library(sf)
library(spdep)
library(rio)

Irrig_Rev_rice_wheat <- import("data/Irrig_Rev_rice_wheat_Updated.csv")

Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$Longitude)))
Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$Latitude)))

library(janitor)
library(tidyr)


Irrig_Rev_rice_wheat$harvest_day_rice <- Irrig_Rev_rice_wheat$l_crop_duration_days_rice + Irrig_Rev_rice_wheat$sowdate_fmt_rice_day

shpname <- file.path(getwd(), "shp", "India_aoi_sf_sp")

India_aoi_sp_bnd <- BayesX::shp2bnd(shpname = shpname, regionnames = "District", check.is.in = F)

Reading map ... finished
Note: map consists originally of 50 polygons
Note: map consists of 47 regions

# Multivariate geoadditive model
# remotes::install_git("https://git.uibk.ac.at/c4031039/mvnchol")
# install_github("https://github.com/meteosimon/mvnchol")
library(mvnchol)

# Remove NAs in the monsoon variables
Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$onset_2017)))
Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$monsoon_onset_dev)))
Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$median_onset_82_15)))
Irrig_Rev_rice_wheat <- subset(Irrig_Rev_rice_wheat, !(is.na(Irrig_Rev_rice_wheat$sd_onset_82_15)))


K <- neighbormatrix(India_aoi_sp_bnd)
head(K)

           Araria Arwal Aurangabad Banka Begusarai Bhagalpur Arah Buxar
Araria          4     0          0     0         0         0    0     0
Arwal           0     6         -1     0         0         0   -1     0
Aurangabad      0    -1          3     0         0         0    0     0
Banka           0     0          0     3         0        -1    0     0
Begusarai       0     0          0     0         5         0    0     0
Bhagalpur       0     0          0    -1         0         6    0     0
           Darbhanga Gaya Gopalganj Jamui Jehanabad Kaimur Katihar Khagaria
Araria             0    0         0     0         0      0       0        0
Arwal              0   -1         0     0        -1      0       0        0
Aurangabad         0   -1         0     0         0      0       0        0
Banka              0    0         0    -1         0      0       0        0
Begusarai          0    0         0     0         0      0       0       -1
Bhagalpur          0    0         0     0         0      0      -1       -1
           Kishanganj Lakhisarai Madhepura Madhubani Munger Muzaffarpur Nalanda
Araria             -1          0        -1         0      0           0       0
Arwal               0          0         0         0      0           0       0
Aurangabad          0          0         0         0      0           0       0
Banka               0          0         0         0     -1           0       0
Begusarai           0         -1         0         0     -1           0       0
Bhagalpur           0          0        -1         0     -1           0       0
           Nawada WestChamparan Patna EastChamparan Purnia Rohtas Saharsa
Araria          0             0     0             0     -1      0       0
Arwal           0             0    -1             0      0     -1       0
Aurangabad      0             0     0             0      0     -1       0
Banka           0             0     0             0      0      0       0
Begusarai       0             0    -1             0      0      0       0
Bhagalpur       0             0     0             0     -1      0       0
           Samastipur Saran Sheikhpura Sheohar Sitamarhi Siwan Supaul Vaishali
Araria              0     0          0       0         0     0     -1        0
Arwal               0     0          0       0         0     0      0        0
Aurangabad          0     0          0       0         0     0      0        0
Banka               0     0          0       0         0     0      0        0
Begusarai          -1     0          0       0         0     0      0        0
Bhagalpur           0     0          0       0         0     0      0        0
           Balia Chandauli Deoria Gazipur Gorakhpur Kushinagar Maharajganj Mau
Araria         0         0      0       0         0          0           0   0
Arwal          0         0      0       0         0          0           0   0
Aurangabad     0         0      0       0         0          0           0   0
Banka          0         0      0       0         0          0           0   0
Begusarai      0         0      0       0         0          0           0   0
Bhagalpur      0         0      0       0         0          0           0   0
           Siddharthnagar
Araria                  0
Arwal                   0
Aurangabad              0
Banka                   0
Begusarai               0
Bhagalpur               0

## Also need to transform to factor for
## setting up the MRF smooth.
Irrig_Rev_rice_wheat$District <- as.factor(Irrig_Rev_rice_wheat$a_q103_district)

## Now note that not all regions are observed,
## therefore we need to remove those regions
## from the penalty matrix
rn <- rownames(K)
lv <- levels(Irrig_Rev_rice_wheat$District)
i <- rn %in% lv
K <- K[i, i]

set.seed(321)
library(bamlss)

2 Non-structural: Bivariate gaussian

2.1 Yield analysis

# Bivariate gaussian 
## Formulas
biv_gauss_yield<- list(
  b_grain_yield_ton_per_ha_rice ~ 1, 
  l_ton_per_hectare ~ 1, 
  sigma1 ~ 1, 
  sigma2 ~ 1,
  rho ~ 1
)

## Model fitting
biv_gauss_yield_model <- bamlss(biv_gauss_yield, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 24596.16 logPost -12332.2 logLik -12293.0 edf 5.0000 eps 0.2442 iteration   1
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0035 iteration   2
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0007 iteration   3
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0000 iteration   4
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0000 iteration   4
elapsed time:  1.05sec
Starting the sampler...

|                    |   0% 29.18min
|*                   |   5% 13.08min 41.32sec
|**                  |  10%  9.86min  1.10min
|***                 |  15%  7.77min  1.37min
|****                |  20%  6.49min  1.62min
|*****               |  25%  6.35min  2.12min
|******              |  30%  5.91min  2.53min
|*******             |  35%  5.10min  2.74min
|********            |  40%  4.47min  2.98min
|*********           |  45%  3.90min  3.19min
|**********          |  50%  3.40min  3.40min
|***********         |  55%  2.96min  3.62min
|************        |  60%  2.57min  3.86min
|*************       |  65%  2.22min  4.12min
|**************      |  70%  1.89min  4.42min
|***************     |  75%  1.56min  4.68min
|****************    |  80%  1.22min  4.90min
|*****************   |  85% 54.06sec  5.11min
|******************  |  90% 35.34sec  5.30min
|******************* |  95% 17.39sec  5.51min
|********************| 100%  0.00sec  5.72min

summary(biv_gauss_yield_model)

Call:
bamlss(formula = biv_gauss_yield, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 4.010 3.978 4.011 4.040       4.01
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula mu2:
---
l_ton_per_hectare ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 2.939 2.913 2.939 2.963      2.939
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula sigma1:
---
sigma1 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.09146 0.07063 0.09140 0.11187      0.091
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9946 0.9615 1.0000     1
---
Formula sigma2:
---
sigma2 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) -0.1987 -0.2187 -0.1986 -0.1787     -0.199
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9946 0.9567 1.0000     1
---
Formula rho:
---
rho ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.1726 0.1436 0.1722 0.2032      0.173
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9925 0.9376 1.0000     1
---
Sampler summary:
-
DIC = 24596.01 logLik = -12295.53 pd = 4.9425
runtime = 344.04
---
Optimizer summary:
-
AICc = 24596.13 edf = 5 logLik = -12293.06
logPost = -12332.19 nobs = 4527 runtime = 1.05

## Prediction
biv_gauss_yield_model_pred <- predict(biv_gauss_yield_model, type = "parameter")

biv_gauss_yield_model_pred= as.data.frame(biv_gauss_yield_model_pred)


# Yield analysis

# Bivariate gaussian 
## Formulas
f_biv_gauss_yld_non_struct <- list(
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  sigma1 ~ 1+rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"), 
  sigma2 ~ 1+ variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  rho ~ 1+s(sowdate_fmt_rice_day)+s(sowdate_fmt_wheat_day)+g_q5305_irrig_times_rice+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)

## Model fitting
biv_gauss_yld_non_struct <- bamlss(f_biv_gauss_yld_non_struct, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 21198.46 logPost -10386.2 logLik -10218.6 edf 350.95 eps 1.2169 iteration   1
AICc 20430.22 logPost -9714.21 logLik -9858.05 edf 330.88 eps 0.4089 iteration   2
AICc 20261.52 logPost -9773.62 logLik -9804.30 edf 304.43 eps 0.1088 iteration   3
AICc 20226.19 logPost -10740.0 logLik -9789.96 edf 301.53 eps 0.0485 iteration   4
AICc 20216.78 logPost -20803.6 logLik -9787.35 edf 299.71 eps 0.0196 iteration   5
AICc 20214.80 logPost -119538. logLik -9786.65 edf 299.46 eps 0.0089 iteration   6
AICc 20214.03 logPost -933316. logLik -9786.44 edf 299.30 eps 0.0067 iteration   7
AICc 20213.68 logPost -4909221 logLik -9786.38 edf 299.20 eps 0.0021 iteration   8
AICc 20213.39 logPost -8764686 logLik -9786.35 edf 299.10 eps 0.0005 iteration   9
AICc 20213.35 logPost -8537899 logLik -9786.34 edf 299.09 eps 0.0004 iteration  10
AICc 20213.33 logPost -8544627 logLik -9786.32 edf 299.10 eps 0.0003 iteration  11
AICc 20213.32 logPost -8545308 logLik -9786.31 edf 299.10 eps 0.0002 iteration  12
AICc 20213.32 logPost -8545376 logLik -9786.31 edf 299.11 eps 0.0001 iteration  13
AICc 20213.31 logPost -8545383 logLik -9786.30 edf 299.11 eps 0.0001 iteration  14
AICc 20213.31 logPost -8545383 logLik -9786.30 edf 299.11 eps 0.0001 iteration  14
elapsed time: 41.41sec
Starting the sampler...

|                    |   0% 56.55min
|*                   |   5% 47.71min  2.51min
|**                  |  10% 43.17min  4.80min
|***                 |  15% 40.33min  7.12min
|****                |  20% 37.77min  9.44min
|*****               |  25% 35.38min 11.79min
|******              |  30% 33.31min 14.28min
|*******             |  35% 30.89min 16.63min
|********            |  40% 28.55min 19.03min
|*********           |  45% 26.60min 21.77min
|**********          |  50% 24.10min 24.10min
|***********         |  55% 21.61min 26.42min
|************        |  60% 19.16min 28.74min
|*************       |  65% 16.79min 31.18min
|**************      |  70% 14.39min 33.58min
|***************     |  75% 11.96min 35.88min
|****************    |  80%  9.63min 38.54min
|*****************   |  85%  7.40min 41.95min
|******************  |  90%  5.03min 45.26min
|******************* |  95%  2.57min 48.74min
|********************| 100%  0.00sec 51.71min

summary(biv_gauss_yld_non_struct)

Call:
bamlss(formula = f_biv_gauss_yld_non_struct, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              3.96382 3.85172 3.96637 4.06918      0.016
rice_duration_class_long 0.07864 0.01476 0.07818 0.14190      0.070
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     6.689e-01 6.478e-02 3.936e-01 2.948e+00
s(sowdate_fmt_rice_day).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       4.150e+00 2.415e+00 4.115e+00 6.181e+00
s(g_q5305_irrig_times_rice).tau21 2.316e+00 4.078e-01 1.589e+00 8.592e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.577e+00 5.099e+00 6.558e+00 8.046e+00
s(nperha_rice).tau21              4.991e-01 3.471e-04 1.492e-01 3.100e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                3.316e+00 1.029e+00 3.160e+00 6.388e+00
s(p2o5perha_rice).tau21           8.241e-02 9.333e-05 4.721e-03 6.202e-01
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             1.784e+00 1.007e+00 1.322e+00 4.526e+00
s(District,id='mrf1').tau21       2.554e-02 3.055e-04 2.171e-02 7.229e-02
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         2.738e+01 6.245e+00 3.115e+01 3.329e+01
s(District,id='re2').tau21        1.031e-01 2.568e-04 9.792e-02 2.658e-01
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          2.790e+01 1.541e+00 3.272e+01 3.439e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.188
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            3.432
s(g_q5305_irrig_times_rice).tau21      3.111
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        7.206
s(nperha_rice).tau21                   1.399
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     5.543
s(p2o5perha_rice).tau21                0.000
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  0.889
s(District,id='mrf1').tau21            0.027
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             31.762
s(District,id='re2').tau21            11.043
s(District,id='re2').alpha                NA
s(District,id='re2').edf              35.908
---
Formula mu2:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                         Mean      2.5%       50%     97.5% parameters
(Intercept)         1.5492388 1.0967330 1.5719162 1.6721103     -1.299
variety_type_NMWV   0.2843960 0.2396195 0.2843188 0.3314649      0.280
g_q5305_irrig_times 0.4012855 0.3753601 0.4009255 0.4287884      0.399
nperha              0.0013300 0.0007374 0.0013327 0.0019225      0.001
p2o5perha           0.0025593 0.0015300 0.0025752 0.0036218      0.003
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 7.396e-02 8.952e-05 3.729e-03 5.398e-01
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   2.017e+00 1.015e+00 1.548e+00 5.106e+00
s(District,id='mrf1').tau21    7.272e-03 5.752e-04 6.149e-03 1.920e-02
s(District,id='mrf1').alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf      2.838e+01 1.637e+01 2.998e+01 3.265e+01
s(District,id='re2').tau21     4.773e-02 2.752e-04 2.191e-02 2.987e-01
s(District,id='re2').alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf       2.729e+01 3.183e+00 3.106e+01 3.517e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21     15.312
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        8.314
s(District,id='mrf1').tau21         0.003
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf          26.699
s(District,id='re2').tau21          5.566
s(District,id='re2').alpha             NA
s(District,id='re2').edf           35.891
---
Formula sigma1:
---
sigma1 ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)              -0.12274 -0.17703 -0.12278 -0.05927     -0.118
rice_duration_class_long  0.06621  0.01722  0.06602  0.11778      0.063
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9844 0.9048 0.9988     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     1.833e-02 7.084e-05 2.519e-03 1.234e-01
s(sowdate_fmt_rice_day).alpha     9.787e-01 8.201e-01 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       1.521e+00 1.009e+00 1.216e+00 3.427e+00
s(g_q5305_irrig_times_rice).tau21 1.159e-01 1.363e-04 4.813e-02 6.030e-01
s(g_q5305_irrig_times_rice).alpha 9.460e-01 6.553e-01 9.946e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   3.414e+00 1.082e+00 3.465e+00 6.141e+00
s(nperha_rice).tau21              1.033e-01 9.987e-05 1.777e-02 7.469e-01
s(nperha_rice).alpha              9.523e-01 6.754e-01 9.960e-01 1.000e+00
s(nperha_rice).edf                2.342e+00 1.013e+00 1.969e+00 5.332e+00
s(p2o5perha_rice).tau21           3.366e-01 9.823e-05 9.507e-03 3.284e+00
s(p2o5perha_rice).alpha           9.497e-01 5.659e-01 9.984e-01 1.000e+00
s(p2o5perha_rice).edf             2.443e+00 1.012e+00 1.737e+00 6.746e+00
s(District,id='mrf1').tau21       2.774e-03 7.698e-05 1.246e-03 1.089e-02
s(District,id='mrf1').alpha       8.358e-01 2.591e-01 9.547e-01 1.000e+00
s(District,id='mrf1').edf         1.827e+01 3.012e+00 1.853e+01 3.047e+01
s(District,id='re2').tau21        1.902e-02 1.412e-04 2.008e-02 4.425e-02
s(District,id='re2').alpha        7.664e-01 1.749e-01 8.783e-01 1.000e+00
s(District,id='re2').edf          2.474e+01 1.340e+00 2.903e+01 3.202e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.000
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            0.873
s(g_q5305_irrig_times_rice).tau21      0.111
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        4.259
s(nperha_rice).tau21                   0.031
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     2.330
s(p2o5perha_rice).tau21                2.333
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  6.388
s(District,id='mrf1').tau21            0.006
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             28.383
s(District,id='re2').tau21             0.000
s(District,id='re2').alpha                NA
s(District,id='re2').edf               0.000
---
Formula sigma2:
---
sigma2 ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -0.7678986 -0.8891231 -0.7662322 -0.6531013     -0.308
variety_type_NMWV    0.2028420  0.1501854  0.2023815  0.2554414      0.196
g_q5305_irrig_times  0.0982535  0.0636687  0.0983932  0.1300880      0.105
nperha              -0.0013030 -0.0019918 -0.0012995 -0.0006358     -0.001
p2o5perha            0.0016906  0.0004414  0.0017003  0.0029155      0.001
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9026 0.4713 0.9777     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 1.215e-01 2.371e-04 4.643e-02 7.535e-01
s(sowdate_fmt_wheat_day).alpha 9.599e-01 7.515e-01 9.960e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   2.688e+00 1.026e+00 2.597e+00 5.178e+00
s(District,id='mrf1').tau21    1.931e-03 7.326e-05 1.205e-03 7.444e-03
s(District,id='mrf1').alpha    8.422e-01 3.277e-01 9.489e-01 1.000e+00
s(District,id='mrf1').edf      1.722e+01 2.961e+00 1.841e+01 2.909e+01
s(District,id='re2').tau21     1.384e-02 3.158e-04 1.383e-02 3.159e-02
s(District,id='re2').alpha     7.828e-01 2.207e-01 8.819e-01 1.000e+00
s(District,id='re2').edf       2.415e+01 2.862e+00 2.700e+01 3.098e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21      0.060
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        2.799
s(District,id='mrf1').tau21         0.000
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf           9.176
s(District,id='re2').tau21          0.191
s(District,id='re2').alpha             NA
s(District,id='re2').edf           34.521
---
Formula rho:
---
rho ~ 1 + s(sowdate_fmt_rice_day) + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times_rice + rice_duration_class_long + variety_type_NMWV + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)               0.1779862  0.0851177  0.1801892  0.2685054      0.019
g_q5305_irrig_times_rice  0.0011476 -0.0129275  0.0008247  0.0170814      0.003
rice_duration_class_long  0.0357800 -0.0391858  0.0384048  0.1053440      0.025
variety_type_NMWV         0.0238027 -0.0489434  0.0209532  0.0997100      0.006
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9510 0.7420 0.9941     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21  8.153e-01 2.087e-04 2.368e-01 5.073e+00
s(sowdate_fmt_rice_day).alpha  9.297e-01 5.299e-01 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf    3.229e+00 1.010e+00 3.273e+00 6.255e+00
s(sowdate_fmt_wheat_day).tau21 7.975e-02 7.837e-05 4.808e-03 5.514e-01
s(sowdate_fmt_wheat_day).alpha 9.739e-01 8.133e-01 9.998e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.604e+00 1.005e+00 1.232e+00 3.872e+00
s(District,id='mrf1').tau21    2.189e-03 8.368e-05 1.777e-03 6.780e-03
s(District,id='mrf1').alpha    8.411e-01 2.759e-01 9.554e-01 1.000e+00
s(District,id='mrf1').edf      1.448e+01 1.625e+00 1.561e+01 2.513e+01
s(District,id='re2').tau21     7.405e-03 1.273e-04 5.477e-03 2.497e-02
s(District,id='re2').alpha     8.518e-01 2.783e-01 9.720e-01 1.000e+00
s(District,id='re2').edf       1.312e+01 5.545e-01 1.374e+01 2.638e+01
                               parameters
s(sowdate_fmt_rice_day).tau21       0.977
s(sowdate_fmt_rice_day).alpha          NA
s(sowdate_fmt_rice_day).edf         4.553
s(sowdate_fmt_wheat_day).tau21      0.101
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        2.658
s(District,id='mrf1').tau21         0.000
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf           3.120
s(District,id='re2').tau21          0.026
s(District,id='re2').alpha             NA
s(District,id='re2').edf           26.409
---
Sampler summary:
-
DIC = 20052.44 logLik = -9924.979 pd = 202.4862
runtime = 3104.76
---
Optimizer summary:
-
AICc = 20213.31 edf = 299.113 logLik = -9786.307
logPost = -8545383 nobs = 4527 runtime = 41.41

par(mfrow = c(2, 3), mar = c(4, 4, 1, 1))
plot(biv_gauss_yld_non_struct, pages = 1, spar = FALSE, rug = TRUE)

## Prediction

2.2 Revenue analysis

# Bivariate gaussian 
## Formulas
biv_gauss_rev <- list(
  revenue_rice ~ 1, 
  revenue_wheat ~ 1, 
  sigma1 ~ 1, 
  sigma2 ~ 1,
  rho ~ 1
)

## Model fitting
biv_gauss_rev_model <- bamlss(biv_gauss_rev, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 200656.7 logPost -102473. logLik -100323. edf 5.0000 eps 0.2543 iteration   1
AICc 200656.6 logPost -102473. logLik -100323. edf 5.0000 eps 0.0045 iteration   2
AICc 200656.6 logPost -102473. logLik -100323. edf 5.0000 eps 0.0002 iteration   3
AICc 200656.6 logPost -102473. logLik -100323. edf 5.0000 eps 0.0000 iteration   4
AICc 200656.6 logPost -102473. logLik -100323. edf 5.0000 eps 0.0000 iteration   4
elapsed time:  0.20sec
Starting the sampler...

|                    |   0%  5.00min
|*                   |   5% 10.04min 31.70sec
|**                  |  10%  8.84min 58.92sec
|***                 |  15%  8.22min  1.45min
|****                |  20%  8.01min  2.00min
|*****               |  25%  7.07min  2.36min
|******              |  30%  6.28min  2.69min
|*******             |  35%  5.81min  3.13min
|********            |  40%  5.42min  3.61min
|*********           |  45%  5.10min  4.18min
|**********          |  50%  4.60min  4.60min
|***********         |  55%  3.96min  4.85min
|************        |  60%  3.38min  5.07min
|*************       |  65%  2.88min  5.34min
|**************      |  70%  2.46min  5.73min
|***************     |  75%  2.03min  6.09min
|****************    |  80%  1.58min  6.30min
|*****************   |  85%  1.15min  6.52min
|******************  |  90% 44.94sec  6.74min
|******************* |  95% 22.17sec  7.02min
|********************| 100%  0.00sec  7.39min

summary(biv_gauss_rev_model)

Call:
bamlss(formula = biv_gauss_rev, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
revenue_rice ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 48710 48702 48709 48714      49953
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 6.800e-04 4.106e-32 1.474e-20     0
---
Formula mu2:
---
revenue_wheat ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 40490 40449 40449 40630      41549
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 3.275e-06 1.309e-22 1.357e-15     0
---
Formula sigma1:
---
sigma1 ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 9.804 9.786 9.804 9.826      9.802
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9939 0.9519 1.0000     1
---
Formula sigma2:
---
sigma2 ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 9.549 9.529 9.549 9.570      9.546
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9945 0.9515 1.0000     1
---
Formula rho:
---
rho ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.2257 0.1958 0.2254 0.2558      0.222
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9923 0.9390 0.9998     1
---
Sampler summary:
-
DIC = 200691.7 logLik = -100344.3 pd = 3.1178
runtime = 443.83
---
Optimizer summary:
-
AICc = 200656.7 edf = 5 logLik = -100323.3
logPost = -102473.3 nobs = 4527 runtime = 0.2

## Prediction
biv_gauss_rev_model_pred <- predict(biv_gauss_rev_model, type = "parameter")

biv_gauss_rev_model_pred= as.data.frame(biv_gauss_rev_model_pred)


# Yield analysis

# Bivariate gaussian 
## Formulas
f_biv_gauss_rev_non_struct <- list(
revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  sigma1 ~ 1+rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"), 
  sigma2 ~ 1+ variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  rho ~ 1+s(sowdate_fmt_rice_day)+s(sowdate_fmt_wheat_day)+g_q5305_irrig_times_rice+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)

## Model fitting
biv_gauss_rev_non_struct <- bamlss(f_biv_gauss_rev_non_struct, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 197935.2 logPost -103564. logLik -98746.9 edf 210.35 eps 0.2673 iteration   1
AICc 197009.3 logPost -116079. logLik -98280.9 edf 213.11 eps 0.3477 iteration   2
AICc 196672.6 logPost -101291. logLik -98111.5 edf 214.06 eps 0.0494 iteration   3
AICc 196577.2 logPost -100754. logLik -98065.1 edf 212.94 eps 0.0196 iteration   4
AICc 196433.4 logPost -102258. logLik -97992.7 edf 213.35 eps 0.0245 iteration   5
AICc 195905.3 logPost -114571. logLik -97704.5 edf 235.18 eps 0.0539 iteration   6
AICc 195321.8 logPost -140909. logLik -97387.8 edf 257.43 eps 0.1751 iteration   7
AICc 195082.0 logPost -324795. logLik -97252.2 edf 271.37 eps 0.0586 iteration   8
AICc 195004.4 logPost -1625241 logLik -97210.9 edf 273.64 eps 0.0207 iteration   9
AICc 194977.7 logPost -3961382 logLik -97197.8 edf 273.36 eps 0.0091 iteration  10
AICc 194965.2 logPost -5444287 logLik -97192.5 edf 272.53 eps 0.0044 iteration  11
AICc 194959.5 logPost -1366094 logLik -97189.6 edf 272.57 eps 0.0032 iteration  12
AICc 194954.9 logPost -9496471 logLik -97187.7 edf 272.25 eps 0.0014 iteration  13
AICc 194951.1 logPost -9078362 logLik -97186.2 edf 271.85 eps 0.0009 iteration  14
AICc 194948.0 logPost -9035974 logLik -97184.8 edf 271.74 eps 0.0009 iteration  15
AICc 194945.0 logPost -9023625 logLik -97183.6 edf 271.47 eps 0.0007 iteration  16
AICc 194941.9 logPost -8937908 logLik -97182.5 edf 271.07 eps 0.0007 iteration  17
AICc 194938.9 logPost -5722880 logLik -97181.5 edf 270.60 eps 0.0003 iteration  18
AICc 194936.4 logPost -4739894 logLik -97180.6 edf 270.33 eps 0.0001 iteration  19
AICc 194935.2 logPost -4657293 logLik -97179.7 edf 270.62 eps 0.0001 iteration  20
AICc 194932.8 logPost -4657648 logLik -97178.7 edf 270.38 eps 0.0001 iteration  21
AICc 194930.3 logPost -4659565 logLik -97177.8 edf 270.09 eps 0.0002 iteration  22
AICc 194927.8 logPost -4662960 logLik -97176.9 edf 269.77 eps 0.0001 iteration  23
AICc 194927.8 logPost -4662960 logLik -97176.9 edf 269.77 eps 0.0001 iteration  23
elapsed time:  1.06min
Starting the sampler...

|                    |   0% 76.54min
|*                   |   5% 63.75min  3.36min
|**                  |  10% 53.59min  5.95min
|***                 |  15% 46.35min  8.18min
|****                |  20% 41.83min 10.46min
|*****               |  25% 38.45min 12.82min
|******              |  30% 35.17min 15.07min
|*******             |  35% 32.42min 17.46min
|********            |  40% 29.62min 19.75min
|*********           |  45% 26.91min 22.02min
|**********          |  50% 24.30min 24.30min
|***********         |  55% 21.72min 26.54min
|************        |  60% 19.17min 28.76min
|*************       |  65% 16.72min 31.05min
|**************      |  70% 14.30min 33.36min
|***************     |  75% 11.90min 35.69min
|****************    |  80%  9.50min 38.01min
|*****************   |  85%  7.10min 40.21min
|******************  |  90%  4.80min 43.23min
|******************* |  95%  2.45min 46.51min
|********************| 100%  0.00sec 49.10min

summary(biv_gauss_rev_non_struct)

Call:
bamlss(formula = f_biv_gauss_rev_non_struct, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)              17195.20  -955.26  1440.39 46047.85      49485
rice_duration_class_long  1788.68   -36.09  1140.15  3866.84       1395
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.5054 0.0000 0.6342     1
-
Smooth terms:
                                        Mean       2.5%        50%      97.5%
s(sowdate_fmt_rice_day).tau21      2.002e+08  2.680e+07  1.359e+08  8.210e+08
s(sowdate_fmt_rice_day).alpha      7.898e-01  0.000e+00  1.000e+00  1.000e+00
s(sowdate_fmt_rice_day).edf       -1.257e+09 -2.795e+08  4.501e+00  6.674e+00
s(g_q5305_irrig_times_rice).tau21  6.952e+08  5.127e+07  3.769e+08  2.414e+09
s(g_q5305_irrig_times_rice).alpha  8.003e-01  0.000e+00  1.000e+00  1.000e+00
s(g_q5305_irrig_times_rice).edf   -4.330e+09 -1.194e+07  6.322e+00  3.135e+06
s(nperha_rice).tau21               5.848e+07  1.396e+01  7.433e+06  2.430e+08
s(nperha_rice).alpha               8.163e-01  0.000e+00  1.000e+00  1.000e+00
s(nperha_rice).edf                 6.296e+18 -1.955e+07  1.696e+00  4.567e+06
s(p2o5perha_rice).tau21            1.041e+07  3.557e+00  2.608e+04  7.463e+07
s(p2o5perha_rice).alpha            7.896e-01  0.000e+00  1.000e+00  1.000e+00
s(p2o5perha_rice).edf             -4.167e+06 -6.829e-01  1.018e+00  5.230e+00
s(District,id='mrf1').tau21        1.222e+06  1.643e-02  4.159e+03  5.419e+06
s(District,id='mrf1').alpha        8.123e-01  0.000e+00  1.000e+00  1.000e+00
s(District,id='mrf1').edf          1.098e+01  6.258e-06  1.380e+00  3.194e+01
s(District,id='re2').tau21         1.585e+09  2.522e+07  1.946e+09  3.910e+09
s(District,id='re2').alpha         8.393e-01  0.000e+00  1.000e+00  1.000e+00
s(District,id='re2').edf           3.529e+01  3.326e+01  3.595e+01  3.598e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21      1.064e+00
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf        1.000e+00
s(g_q5305_irrig_times_rice).tau21  3.435e+09
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    8.414e+00
s(nperha_rice).tau21               8.620e-01
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 1.000e+00
s(p2o5perha_rice).tau21            9.890e-01
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              1.000e+00
s(District,id='mrf1').tau21        8.703e+06
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          3.292e+01
s(District,id='re2').tau21         1.467e+02
s(District,id='re2').alpha                NA
s(District,id='re2').edf           1.005e+00
---
Formula mu2:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                        Mean     2.5%      50%    97.5% parameters
(Intercept)         18202.41 18077.02 18213.80 18576.42   22156.71
variety_type_NMWV    4561.08  4441.50  4472.89  4732.72    3985.03
g_q5305_irrig_times  6085.64  5898.43  6079.41  6165.28    5448.19
nperha                 29.16    25.62    29.70    32.41      17.31
p2o5perha              64.05    60.73    63.06    67.99      53.36
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 2.946e-04 0.000e+00 3.215e-20     0
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 5.701e+06 4.570e+01 3.632e+04 5.124e+07
s(sowdate_fmt_wheat_day).alpha 9.823e-01 9.785e-01 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.546e+00 9.974e-01 1.035e+00 4.331e+00
s(District,id='mrf1').tau21    1.231e+07 5.890e+06 1.168e+07 2.143e+07
s(District,id='mrf1').alpha    9.941e-01 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf      3.365e+01 3.225e+01 3.383e+01 3.445e+01
s(District,id='re2').tau21     8.841e+01 1.114e-04 1.069e-01 7.423e+02
s(District,id='re2').alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf       1.667e-01 1.560e-08 4.273e-05 1.033e+00
                               parameters
s(sowdate_fmt_wheat_day).tau21  3.155e+07
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf    4.207e+00
s(District,id='mrf1').tau21     9.168e+07
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf       3.487e+01
s(District,id='re2').tau21      6.421e+01
s(District,id='re2').alpha             NA
s(District,id='re2').edf        9.940e-01
---
Formula sigma1:
---
sigma1 ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)               1.28478 -0.02742  1.06988  2.41061     -0.055
rice_duration_class_long  0.12742  0.07107  0.12707  0.18178      0.127
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9847 0.8917 0.9996     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     8.091e-02 1.282e-04 1.781e-02 4.694e-01
s(sowdate_fmt_rice_day).alpha     9.583e-01 6.617e-01 9.980e-01 1.000e+00
s(sowdate_fmt_rice_day).edf       2.142e+00 1.014e+00 1.914e+00 4.478e+00
s(g_q5305_irrig_times_rice).tau21 4.214e-01 2.334e-04 2.240e-01 1.841e+00
s(g_q5305_irrig_times_rice).alpha 9.282e-01 6.091e-01 9.876e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   4.628e+00 1.098e+00 4.936e+00 7.375e+00
s(nperha_rice).tau21              4.299e-01 3.373e-04 9.419e-02 2.857e+00
s(nperha_rice).alpha              8.967e-01 2.872e-01 9.869e-01 1.000e+00
s(nperha_rice).edf                3.406e+00 1.031e+00 3.121e+00 6.991e+00
s(p2o5perha_rice).tau21           2.938e-01 1.519e-04 2.890e-02 2.397e+00
s(p2o5perha_rice).alpha           9.364e-01 4.635e-01 9.937e-01 1.000e+00
s(p2o5perha_rice).edf             2.746e+00 1.018e+00 2.318e+00 6.546e+00
s(District,id='mrf1').tau21       1.143e-02 9.768e-05 4.155e-03 4.826e-02
s(District,id='mrf1').alpha       7.856e-01 1.830e-01 9.117e-01 1.000e+00
s(District,id='mrf1').edf         2.344e+01 4.003e+00 2.705e+01 3.346e+01
s(District,id='re2').tau21        7.243e+01 3.746e+01 6.883e+01 1.355e+02
s(District,id='re2').alpha        5.746e-01 1.083e-07 5.891e-01 1.000e+00
s(District,id='re2').edf          3.599e+01 3.598e+01 3.599e+01 3.600e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21      0.000e+00
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf        8.740e-01
s(g_q5305_irrig_times_rice).tau21  9.780e-01
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    6.514e+00
s(nperha_rice).tau21               4.083e+00
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 7.349e+00
s(p2o5perha_rice).tau21            0.000e+00
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              1.008e+00
s(District,id='mrf1').tau21        2.000e-03
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          2.302e+01
s(District,id='re2').tau21         7.395e+05
s(District,id='re2').alpha                NA
s(District,id='re2').edf           3.600e+01
---
Formula sigma2:
---
sigma2 ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)          3.177e+00  6.503e-01  3.604e+00  4.562e+00     -0.253
variety_type_NMWV    1.409e-01  8.946e-02  1.406e-01  1.932e-01      0.148
g_q5305_irrig_times  1.066e-01  7.347e-02  1.071e-01  1.402e-01      0.112
nperha              -7.542e-04 -1.433e-03 -7.518e-04 -6.468e-05     -0.001
p2o5perha            1.756e-03  5.079e-04  1.751e-03  3.072e-03      0.002
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9042 0.4680 0.9884     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 2.297e-01 1.107e-03 1.036e-01 1.192e+00
s(sowdate_fmt_wheat_day).alpha 9.454e-01 6.573e-01 9.944e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   3.314e+00 1.131e+00 3.293e+00 5.706e+00
s(District,id='mrf1').tau21    1.733e-02 9.097e-05 9.260e-03 6.888e-02
s(District,id='mrf1').alpha    7.371e-01 1.141e-01 8.376e-01 1.000e+00
s(District,id='mrf1').edf      2.540e+01 3.733e+00 3.016e+01 3.372e+01
s(District,id='re2').tau21     3.638e+01 1.464e+01 3.150e+01 8.423e+01
s(District,id='re2').alpha     5.491e-01 1.355e-05 5.286e-01 1.000e+00
s(District,id='re2').edf       3.598e+01 3.596e+01 3.598e+01 3.599e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21      0.204
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        3.850
s(District,id='mrf1').tau21         0.003
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf          24.676
s(District,id='re2').tau21         44.148
s(District,id='re2').alpha             NA
s(District,id='re2').edf           35.987
---
Formula rho:
---
rho ~ 1 + s(sowdate_fmt_rice_day) + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times_rice + rice_duration_class_long + variety_type_NMWV + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)               0.2160157  0.1298578  0.2170445  0.3006881      0.189
g_q5305_irrig_times_rice -0.0008824 -0.0162220 -0.0008467  0.0161686      0.000
rice_duration_class_long  0.0808665  0.0086175  0.0816641  0.1569372      0.082
variety_type_NMWV        -0.0096978 -0.0856637 -0.0095616  0.0651296     -0.018
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9516 0.7338 0.9974     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21  2.296e-01 1.379e-04 3.616e-02 1.792e+00
s(sowdate_fmt_rice_day).alpha  9.638e-01 7.356e-01 9.986e-01 1.000e+00
s(sowdate_fmt_rice_day).edf    2.244e+00 1.005e+00 1.897e+00 5.140e+00
s(sowdate_fmt_wheat_day).tau21 4.620e-02 8.680e-05 4.230e-03 3.536e-01
s(sowdate_fmt_wheat_day).alpha 9.583e-01 6.648e-01 9.987e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.522e+00 1.006e+00 1.220e+00 3.457e+00
s(District,id='mrf1').tau21    3.844e-03 1.520e-04 3.540e-03 9.680e-03
s(District,id='mrf1').alpha    8.069e-01 2.230e-01 9.226e-01 1.000e+00
s(District,id='mrf1').edf      1.879e+01 3.235e+00 2.095e+01 2.702e+01
s(District,id='re2').tau21     8.225e-03 9.748e-05 4.168e-03 3.336e-02
s(District,id='re2').alpha     8.697e-01 2.799e-01 9.919e-01 1.000e+00
s(District,id='re2').edf       1.244e+01 3.988e-01 1.208e+01 2.742e+01
                               parameters
s(sowdate_fmt_rice_day).tau21       0.035
s(sowdate_fmt_rice_day).alpha          NA
s(sowdate_fmt_rice_day).edf         1.890
s(sowdate_fmt_wheat_day).tau21      0.000
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        0.851
s(District,id='mrf1').tau21         0.006
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf          24.345
s(District,id='re2').tau21          0.000
s(District,id='re2').alpha             NA
s(District,id='re2').edf            0.000
---
Sampler summary:
-
DIC = -8046167 logLik = -97308.74 pd = -8240785
runtime = 2948.71
---
Optimizer summary:
-
AICc = 194927.8 edf = 269.7733 logLik = -97176.98
logPost = -4662961 nobs = 4527 runtime = 63.72

par(mfrow = c(2, 3), mar = c(4, 4, 1, 1))
plot(biv_gauss_rev_non_struct, pages = 1, spar = FALSE, rug = TRUE)

## Prediction
biv_gauss_rev_non_struct_pred <- predict(biv_gauss_rev_non_struct, type = "parameter")

biv_gauss_rev_non_struct_pred= as.data.frame(biv_gauss_rev_non_struct_pred)

#Structural: Bivariate gaussian

##First stage

f_sow_rice_1st_stage <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re")
)

f_sow_rice_1st_stage_MRF <- bamlss(f_sow_rice_1st_stage, data = Irrig_Rev_rice_wheat, family = "gaussian")

AICc 38862.03 logPost -165306. logLik -19371.2 edf 59.010 eps 0.1226 iteration   1
AICc 34841.08 logPost -31072.7 logLik -17339.3 edf 79.788 eps 0.0980 iteration   2
AICc 33498.94 logPost -18399.0 logLik -16648.2 edf 98.970 eps 0.0632 iteration   3
AICc 33180.98 logPost -17093.4 logLik -16491.0 edf 97.287 eps 0.0297 iteration   4
AICc 33096.83 logPost -16986.5 logLik -16452.6 edf 93.751 eps 0.0069 iteration   5
AICc 33056.53 logPost -16935.2 logLik -16435.7 edf 90.674 eps 0.0017 iteration   6
AICc 33040.37 logPost -16899.0 logLik -16429.8 edf 88.587 eps 0.0009 iteration   7
AICc 33035.63 logPost -16869.0 logLik -16428.1 edf 87.868 eps 0.0003 iteration   8
AICc 33028.91 logPost -16845.9 logLik -16427.6 edf 85.110 eps 0.0001 iteration   9
AICc 33028.60 logPost -16840.2 logLik -16427.5 edf 85.077 eps 0.0000 iteration  10
AICc 33028.60 logPost -16840.2 logLik -16427.5 edf 85.077 eps 0.0000 iteration  10
elapsed time:  5.08sec
Starting the sampler...

|                    |   0%  1.21min
|*                   |   5%  1.42min  4.48sec
|**                  |  10%  1.73min 11.51sec
|***                 |  15%  1.89min 19.98sec
|****                |  20%  1.81min 27.14sec
|*****               |  25%  1.72min 34.34sec
|******              |  30%  1.64min 42.17sec
|*******             |  35%  1.55min 50.20sec
|********            |  40%  1.52min  1.02min
|*********           |  45%  1.44min  1.17min
|**********          |  50%  1.31min  1.31min
|***********         |  55%  1.19min  1.46min
|************        |  60%  1.08min  1.62min
|*************       |  65% 56.16sec  1.74min
|**************      |  70% 45.97sec  1.79min
|***************     |  75% 36.76sec  1.84min
|****************    |  80% 28.31sec  1.89min
|*****************   |  85% 20.54sec  1.94min
|******************  |  90% 13.25sec  1.99min
|******************* |  95%  6.44sec  2.04min
|********************| 100%  0.00sec  2.09min

fitted_f_sow_rice_1st_stage_MRF <- f_sow_rice_1st_stage_MRF$fitted

Irrig_Rev_rice_wheat$Res_rice_sow <- Irrig_Rev_rice_wheat$sowdate_fmt_rice_day - fitted_f_sow_rice_1st_stage_MRF$mu

# Wheat first stage
f_sow_wheat_1st_stage <- list(
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(gw_2018) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re")
)

f_sow_wheat_1st_stage_MRF <- bamlss(f_sow_wheat_1st_stage, data = Irrig_Rev_rice_wheat, family = "gaussian")

AICc 49188.65 logPost -488850. logLik -24543.4 edf 50.285 eps 0.2566 iteration   1
AICc 44824.42 logPost -64385.9 logLik -22386.0 edf 26.046 eps 0.0753 iteration   2
AICc 40409.05 logPost -24539.6 logLik -20136.0 edf 67.444 eps 0.0824 iteration   3
AICc 36648.46 logPost -18973.1 logLik -18246.6 edf 76.219 eps 0.0789 iteration   4
AICc 33900.77 logPost -17313.2 logLik -16871.9 edf 77.104 eps 0.0796 iteration   5
AICc 32636.01 logPost -16736.4 logLik -16238.1 edf 78.490 eps 0.0660 iteration   6
AICc 32419.72 logPost -16629.9 logLik -16129.2 edf 79.163 eps 0.0324 iteration   7
AICc 32413.31 logPost -16627.4 logLik -16125.7 edf 79.502 eps 0.0056 iteration   8
AICc 32412.92 logPost -16627.3 logLik -16125.4 edf 79.574 eps 0.0001 iteration   9
AICc 32412.79 logPost -16627.2 logLik -16125.3 edf 79.581 eps 0.0000 iteration  10
AICc 32412.79 logPost -16627.2 logLik -16125.3 edf 79.581 eps 0.0000 iteration  10
elapsed time:  2.58sec
Starting the sampler...

|                    |   0% 46.41sec
|*                   |   5% 51.68sec  2.72sec
|**                  |  10% 50.85sec  5.65sec
|***                 |  15% 48.34sec  8.53sec
|****                |  20% 44.12sec 11.03sec
|*****               |  25% 40.44sec 13.48sec
|******              |  30% 42.77sec 18.33sec
|*******             |  35% 52.48sec 28.26sec
|********            |  40% 53.88sec 35.92sec
|*********           |  45% 51.35sec 42.01sec
|**********          |  50% 48.17sec 48.17sec
|***********         |  55% 44.71sec 54.65sec
|************        |  60% 39.91sec 59.86sec
|*************       |  65% 33.87sec  1.05min
|**************      |  70% 28.26sec  1.10min
|***************     |  75% 23.05sec  1.15min
|****************    |  80% 18.08sec  1.21min
|*****************   |  85% 13.31sec  1.26min
|******************  |  90%  8.75sec  1.31min
|******************* |  95%  4.31sec  1.37min
|********************| 100%  0.00sec  1.42min

fitted_f_sow_wheat_1st_stage_MRF <- f_sow_wheat_1st_stage_MRF$fitted

Irrig_Rev_rice_wheat$Res_wheat_sow <- Irrig_Rev_rice_wheat$sowdate_fmt_wheat_day - fitted_f_sow_wheat_1st_stage_MRF$mu

2.3 Second stage: Yield

f_biv_gauss_yld_struct <- list(
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  sigma1 ~ 1+rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"), 
  sigma2 ~ 1+ variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  rho ~ 1+s(Res_rice_sow)+s(Res_wheat_sow)+g_q5305_irrig_times_rice+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)

## Model fitting
biv_gauss_yld_struct <- bamlss(f_biv_gauss_yld_struct, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 21126.23 logPost -10396.1 logLik -10173.6 edf 358.50 eps 1.1013 iteration   1
AICc 20396.55 logPost -9707.49 logLik -9845.48 edf 327.21 eps 0.5602 iteration   2
AICc 20286.20 logPost -10303.0 logLik -9816.07 edf 304.93 eps 0.1497 iteration   3
AICc 20265.83 logPost -17725.4 logLik -9811.48 edf 300.05 eps 0.0313 iteration   4
AICc 20262.13 logPost -91299.1 logLik -9810.80 edf 299.03 eps 0.0195 iteration   5
AICc 20261.79 logPost -686320. logLik -9810.65 edf 299.02 eps 0.0062 iteration   6
AICc 20261.70 logPost -2720911 logLik -9810.62 edf 299.00 eps 0.0004 iteration   7
AICc 20261.30 logPost -6475517 logLik -9810.60 edf 298.84 eps 0.0002 iteration   8
AICc 20260.82 logPost -1057981 logLik -9810.59 edf 298.64 eps 0.0002 iteration   9
AICc 20260.76 logPost -1064390 logLik -9810.58 edf 298.62 eps 0.0002 iteration  10
AICc 20260.76 logPost -1065095 logLik -9810.58 edf 298.63 eps 0.0006 iteration  11
AICc 20260.78 logPost -1065166 logLik -9810.57 edf 298.64 eps 0.0001 iteration  12
AICc 20260.79 logPost -1065172 logLik -9810.57 edf 298.65 eps 0.0000 iteration  13
AICc 20260.79 logPost -1065172 logLik -9810.57 edf 298.65 eps 0.0000 iteration  13
elapsed time:  1.03min
Starting the sampler...

|                    |   0% 47.36min
|*                   |   5% 62.84min  3.31min
|**                  |  10% 56.38min  6.26min
|***                 |  15% 53.74min  9.48min
|****                |  20% 50.21min 12.55min
|*****               |  25% 47.16min 15.72min
|******              |  30% 43.87min 18.80min
|*******             |  35% 40.71min 21.92min
|********            |  40% 37.31min 24.87min
|*********           |  45% 34.18min 27.97min
|**********          |  50% 30.84min 30.84min
|***********         |  55% 27.68min 33.83min
|************        |  60% 24.66min 36.98min
|*************       |  65% 21.51min 39.95min
|**************      |  70% 18.38min 42.88min
|***************     |  75% 15.30min 45.89min
|****************    |  80% 12.34min 49.37min
|*****************   |  85%  9.28min 52.59min
|******************  |  90%  6.23min 56.08min
|******************* |  95%  3.11min 59.15min
|********************| 100%  0.00sec 62.12min

summary(biv_gauss_yld_struct)

Call:
bamlss(formula = f_biv_gauss_yld_struct, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              3.95335 3.81644 3.95522 4.08772      0.005
rice_duration_class_long 0.09107 0.02731 0.09176 0.15245      0.088
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             8.131e-01 2.158e-02 3.569e-01 4.159e+00
s(Res_rice_sow).alpha             1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Res_rice_sow).edf               4.227e+00 1.765e+00 4.169e+00 7.117e+00
s(g_q5305_irrig_times_rice).tau21 2.175e+00 3.612e-01 1.531e+00 8.304e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.500e+00 4.825e+00 6.540e+00 7.947e+00
s(nperha_rice).tau21              6.055e-01 1.926e-03 2.238e-01 3.179e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                3.685e+00 1.102e+00 3.591e+00 6.677e+00
s(p2o5perha_rice).tau21           8.949e-02 9.721e-05 7.386e-03 5.326e-01
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             1.831e+00 1.009e+00 1.437e+00 4.237e+00
s(District,id='mrf1').tau21       1.802e-02 9.875e-05 1.210e-02 5.933e-02
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         2.491e+01 2.348e+00 2.938e+01 3.309e+01
s(District,id='re2').tau21        1.186e-01 3.505e-04 1.193e-01 2.714e-01
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.041e+01 1.768e+00 3.313e+01 3.442e+01
                                  parameters
s(Res_rice_sow).tau21                  4.418
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                    7.212
s(g_q5305_irrig_times_rice).tau21      2.737
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        7.089
s(nperha_rice).tau21                   1.193
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     5.364
s(p2o5perha_rice).tau21                0.000
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  0.890
s(District,id='mrf1').tau21            0.026
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             31.701
s(District,id='re2').tau21            11.172
s(District,id='re2').alpha                NA
s(District,id='re2').edf              35.910
---
Formula mu2:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                         Mean      2.5%       50%     97.5% parameters
(Intercept)         1.5308628 1.4244975 1.5317955 1.6269497     -1.337
variety_type_NMWV   0.3430966 0.3009355 0.3431098 0.3852078      0.337
g_q5305_irrig_times 0.4030616 0.3769073 0.4032167 0.4286351      0.400
nperha              0.0014576 0.0008931 0.0014491 0.0020108      0.001
p2o5perha           0.0025066 0.0014580 0.0025052 0.0035692      0.002
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      1.451e-02 7.341e-05 2.093e-03 1.193e-01      0.000
s(Res_wheat_sow).alpha      1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.560e+00 1.012e+00 1.243e+00 3.685e+00      0.996
s(District,id='mrf1').tau21 1.503e-02 4.148e-03 1.467e-02 2.835e-02      0.006
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.180e+01 2.836e+01 3.223e+01 3.321e+01     30.073
s(District,id='re2').tau21  1.384e-02 7.866e-05 6.538e-03 5.756e-02      6.208
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    2.062e+01 1.177e+00 2.404e+01 3.346e+01     35.907
---
Formula sigma1:
---
sigma1 ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + 
    s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)              -0.12208 -0.18031 -0.12330 -0.06052     -0.124
rice_duration_class_long  0.07049  0.02023  0.07108  0.12041      0.068
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9875 0.9058 1.0000     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             1.759e-02 6.674e-05 2.363e-03 1.380e-01
s(Res_rice_sow).alpha             9.733e-01 8.111e-01 9.987e-01 1.000e+00
s(Res_rice_sow).edf               1.531e+00 1.008e+00 1.223e+00 3.800e+00
s(g_q5305_irrig_times_rice).tau21 1.351e-01 1.527e-04 4.886e-02 7.771e-01
s(g_q5305_irrig_times_rice).alpha 9.535e-01 7.063e-01 9.966e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   3.447e+00 1.081e+00 3.539e+00 6.222e+00
s(nperha_rice).tau21              9.353e-02 1.089e-04 1.829e-02 6.611e-01
s(nperha_rice).alpha              9.584e-01 7.172e-01 9.984e-01 1.000e+00
s(nperha_rice).edf                2.333e+00 1.012e+00 2.051e+00 5.151e+00
s(p2o5perha_rice).tau21           2.151e-01 9.922e-05 6.857e-03 2.038e+00
s(p2o5perha_rice).alpha           9.580e-01 6.301e-01 9.995e-01 1.000e+00
s(p2o5perha_rice).edf             2.209e+00 1.014e+00 1.532e+00 6.215e+00
s(District,id='mrf1').tau21       2.212e-03 6.469e-05 9.503e-04 9.380e-03
s(District,id='mrf1').alpha       8.402e-01 2.826e-01 9.379e-01 1.000e+00
s(District,id='mrf1').edf         1.673e+01 2.880e+00 1.634e+01 3.020e+01
s(District,id='re2').tau21        2.098e-02 3.454e-04 2.114e-02 4.457e-02
s(District,id='re2').alpha        7.642e-01 1.799e-01 8.447e-01 1.000e+00
s(District,id='re2').edf          2.674e+01 3.053e+00 2.928e+01 3.214e+01
                                  parameters
s(Res_rice_sow).tau21                  0.000
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                    0.873
s(g_q5305_irrig_times_rice).tau21      0.118
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        4.319
s(nperha_rice).tau21                   0.026
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     2.204
s(p2o5perha_rice).tau21                2.179
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  6.310
s(District,id='mrf1').tau21            0.006
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             28.495
s(District,id='re2').tau21             0.000
s(District,id='re2').alpha                NA
s(District,id='re2').edf               0.000
---
Formula sigma2:
---
sigma2 ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -0.7779709 -0.8885843 -0.7769707 -0.6691374     -0.307
variety_type_NMWV    0.2184419  0.1690054  0.2190007  0.2710299      0.211
g_q5305_irrig_times  0.0951245  0.0635572  0.0947395  0.1258895      0.096
nperha              -0.0012210 -0.0018850 -0.0012250 -0.0005307     -0.001
p2o5perha            0.0017190  0.0004498  0.0017051  0.0029586      0.001
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9020 0.4867 0.9814     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      4.801e-01 2.713e-04 1.514e-01 2.754e+00      1.556
s(Res_wheat_sow).alpha      9.225e-01 5.257e-01 9.919e-01 1.000e+00         NA
s(Res_wheat_sow).edf        3.707e+00 1.033e+00 3.662e+00 7.004e+00      6.225
s(District,id='mrf1').tau21 1.892e-03 6.259e-05 1.229e-03 6.047e-03      0.000
s(District,id='mrf1').alpha 8.381e-01 2.941e-01 9.445e-01 1.000e+00         NA
s(District,id='mrf1').edf   1.751e+01 2.705e+00 1.893e+01 2.868e+01      7.640
s(District,id='re2').tau21  1.213e-02 2.028e-04 1.188e-02 2.816e-02      0.188
s(District,id='re2').alpha  7.870e-01 2.070e-01 8.925e-01 1.000e+00         NA
s(District,id='re2').edf    2.306e+01 1.861e+00 2.608e+01 3.075e+01     34.508
---
Formula rho:
---
rho ~ 1 + s(Res_rice_sow) + s(Res_wheat_sow) + g_q5305_irrig_times_rice + 
    rice_duration_class_long + variety_type_NMWV + s(District, 
    bs = "mrf", xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)               0.1846639  0.1025717  0.1859839  0.2718087      0.006
g_q5305_irrig_times_rice -0.0008777 -0.0157905 -0.0006756  0.0139846      0.000
rice_duration_class_long  0.0217284 -0.0471363  0.0219395  0.0920891      0.023
variety_type_NMWV         0.0454186 -0.0254043  0.0459622  0.1111607      0.027
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9508 0.7330 0.9961     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_rice_sow).tau21       2.342e-01 8.786e-05 6.623e-03 2.272e+00      3.119
s(Res_rice_sow).alpha       9.631e-01 7.087e-01 9.994e-01 1.000e+00         NA
s(Res_rice_sow).edf         1.967e+00 1.004e+00 1.304e+00 6.303e+00      6.305
s(Res_wheat_sow).tau21      3.540e-02 7.767e-05 2.916e-03 2.808e-01      0.000
s(Res_wheat_sow).alpha      9.732e-01 8.040e-01 9.983e-01 1.000e+00         NA
s(Res_wheat_sow).edf        1.423e+00 1.004e+00 1.136e+00 3.502e+00      0.764
s(District,id='mrf1').tau21 1.770e-03 7.871e-05 1.455e-03 5.594e-03      0.000
s(District,id='mrf1').alpha 8.527e-01 3.361e-01 9.619e-01 1.000e+00         NA
s(District,id='mrf1').edf   1.324e+01 1.563e+00 1.432e+01 2.375e+01      0.000
s(District,id='re2').tau21  5.459e-03 9.072e-05 3.154e-03 1.999e-02      0.033
s(District,id='re2').alpha  8.907e-01 4.008e-01 9.933e-01 1.000e+00         NA
s(District,id='re2').edf    1.072e+01 3.999e-01 9.933e+00 2.462e+01     27.869
---
Sampler summary:
-
DIC = 20094.06 logLik = -9947.8 pd = 198.4613
runtime = 3728.94
---
Optimizer summary:
-
AICc = 20260.79 edf = 298.6534 logLik = -9810.573
logPost = -10651724 nobs = 4527 runtime = 61.86

par(mfrow = c(2, 3), mar = c(4, 4, 1, 1))
plot(biv_gauss_yld_struct, pages = 1, spar = FALSE, rug = TRUE)

dev.off()

null device 
          1 

3 Second stage: Revenue

f_biv_gauss_rev_struct <- list(
revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  sigma1 ~ 1+rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"), 
  sigma2 ~ 1+ variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  rho ~ 1+s(Res_rice_sow)+s(Res_wheat_sow)+g_q5305_irrig_times_rice+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)

## Model fitting
biv_gauss_rev_struct <- bamlss(f_biv_gauss_rev_struct, family = bamlss:::bivnorm_bamlss, data = Irrig_Rev_rice_wheat,
  burnin = 2000, thin = 10, n.iter = 12000, sampler = TRUE, nu = 1)

AICc 198308.9 logPost -103699. logLik -98929.8 edf 213.95 eps 0.2649 iteration   1
AICc 197342.4 logPost -101701. logLik -98450.7 edf 210.19 eps 0.4409 iteration   2
AICc 197093.9 logPost -104847. logLik -98322.1 edf 214.16 eps 0.0946 iteration   3
AICc 197028.0 logPost -138001. logLik -98286.2 edf 216.79 eps 0.1044 iteration   4
AICc 196808.5 logPost -464658. logLik -98174.8 edf 218.34 eps 0.0537 iteration   5
AICc 196067.3 logPost -2879026 logLik -97781.9 edf 238.44 eps 0.1130 iteration   6
AICc 195372.9 logPost -2191541 logLik -97410.1 edf 260.31 eps 0.1442 iteration   7
AICc 195114.1 logPost -765628. logLik -97266.8 edf 272.67 eps 0.0856 iteration   8
AICc 195042.8 logPost -794515. logLik -97227.6 edf 275.81 eps 0.0312 iteration   9
AICc 195010.3 logPost -905464. logLik -97215.3 edf 272.32 eps 0.0066 iteration  10
AICc 195001.0 logPost -1148572 logLik -97210.4 edf 272.51 eps 0.0031 iteration  11
AICc 194997.7 logPost -3862029 logLik -97207.9 edf 273.33 eps 0.0023 iteration  12
AICc 194994.1 logPost -2482588 logLik -97206.1 edf 273.30 eps 0.0012 iteration  13
AICc 194990.9 logPost -2230374 logLik -97204.7 edf 273.11 eps 0.0006 iteration  14
AICc 194987.8 logPost -2201978 logLik -97203.5 edf 272.87 eps 0.0003 iteration  15
AICc 194985.0 logPost -2198884 logLik -97202.3 edf 272.58 eps 0.0002 iteration  16
AICc 194982.6 logPost -4645874 logLik -97201.3 edf 272.45 eps 0.0003 iteration  17
AICc 194980.9 logPost -3331716 logLik -97200.3 edf 272.60 eps 0.0001 iteration  18
AICc 194979.9 logPost -3219915 logLik -97199.3 edf 273.01 eps 0.0001 iteration  19
AICc 194977.8 logPost -3220790 logLik -97198.4 edf 272.90 eps 0.0002 iteration  20
AICc 194975.5 logPost -3223686 logLik -97197.4 edf 272.74 eps 0.0001 iteration  21
AICc 194973.2 logPost -3228658 logLik -97196.5 edf 272.57 eps 0.0000 iteration  22
AICc 194973.2 logPost -3228658 logLik -97196.5 edf 272.57 eps 0.0000 iteration  22
elapsed time:  1.54min
Starting the sampler...

|                    |   0% 48.56min
|*                   |   5% 64.07min  3.37min
|**                  |  10% 53.53min  5.95min
|***                 |  15% 49.61min  8.75min
|****                |  20% 46.45min 11.61min
|*****               |  25% 44.69min 14.90min
|******              |  30% 43.76min 18.76min
|*******             |  35% 39.84min 21.45min
|********            |  40% 36.54min 24.36min
|*********           |  45% 33.33min 27.27min
|**********          |  50% 30.29min 30.29min
|***********         |  55% 27.34min 33.42min
|************        |  60% 24.21min 36.32min
|*************       |  65% 21.22min 39.42min
|**************      |  70% 19.55min 45.63min
|***************     |  75% 15.96min 47.87min
|****************    |  80% 12.74min 50.95min
|*****************   |  85% 10.09min 57.20min
|******************  |  90%  6.62min 59.58min
|******************* |  95%  3.29min 62.57min
|********************| 100%  0.00sec 69.03min

summary(biv_gauss_rev_struct)

Call:
bamlss(formula = f_biv_gauss_rev_struct, family = bamlss:::bivnorm_bamlss, 
    data = Irrig_Rev_rice_wheat, sampler = TRUE, burnin = 2000, 
    thin = 10, n.iter = 12000, nu = 1)
---
Family: mvnorm 
Link function: mu1 = identity, mu2 = identity, sigma1 = log, sigma2 = log, rho = rhogit
*---
Formula mu1:
---
revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)               5702.08 -1284.02   818.59 44328.19      49416
rice_duration_class_long  1148.56    77.52   973.06  3739.25       1447
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.6541 0.0000 0.8783     1
-
Smooth terms:
                                        Mean       2.5%        50%      97.5%
s(Res_rice_sow).tau21              1.755e+08  6.591e+06  6.628e+07  8.470e+08
s(Res_rice_sow).alpha              8.992e-01  0.000e+00  1.000e+00  1.000e+00
s(Res_rice_sow).edf                4.804e+06 -7.399e+06  4.137e+00  7.274e+00
s(g_q5305_irrig_times_rice).tau21  3.695e+08  4.557e+07  2.256e+08  1.406e+09
s(g_q5305_irrig_times_rice).alpha  8.824e-01  0.000e+00  1.000e+00  1.000e+00
s(g_q5305_irrig_times_rice).edf   -6.474e+06 -9.290e+06  6.238e+00  7.847e+00
s(nperha_rice).tau21               2.784e+07  7.054e+00  4.813e+05  2.507e+08
s(nperha_rice).alpha               9.067e-01  0.000e+00  1.000e+00  1.000e+00
s(nperha_rice).edf                -4.909e+06  7.998e-01  1.116e+00  5.667e+00
s(p2o5perha_rice).tau21            2.367e+07  4.913e+00  5.205e+04  1.913e+08
s(p2o5perha_rice).alpha            9.041e-01  0.000e+00  1.000e+00  1.000e+00
s(p2o5perha_rice).edf             -3.288e+06  2.132e-01  1.029e+00  5.032e+00
s(District,id='mrf1').tau21        1.092e+06  5.811e+00  3.583e+04  8.739e+06
s(District,id='mrf1').alpha        9.478e-01  0.000e+00  1.000e+00  1.000e+00
s(District,id='mrf1').edf          1.041e+01  3.572e-02  4.494e+00  3.278e+01
s(District,id='re2').tau21         2.148e+09  5.358e+07  2.225e+09  3.847e+09
s(District,id='re2').alpha         9.770e-01  8.125e-01  1.000e+00  1.000e+00
s(District,id='re2').edf           3.582e+01  3.461e+01  3.596e+01  3.598e+01
                                  parameters
s(Res_rice_sow).tau21              2.278e+00
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                1.000e+00
s(g_q5305_irrig_times_rice).tau21  2.594e+09
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    8.277e+00
s(nperha_rice).tau21               1.039e+00
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 1.000e+00
s(p2o5perha_rice).tau21            1.266e+00
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              1.000e+00
s(District,id='mrf1').tau21        9.153e+06
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          3.302e+01
s(District,id='re2').tau21         1.096e+02
s(District,id='re2').alpha                NA
s(District,id='re2').edf           1.003e+00
---
Formula mu2:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                        Mean     2.5%      50%    97.5% parameters
(Intercept)         17906.90 17832.38 17923.93 18236.71   21382.96
variety_type_NMWV    4576.08  4474.97  4474.97  4862.21    4883.99
g_q5305_irrig_times  6003.36  5928.65  5928.65  6184.35    5460.99
nperha                 31.72    26.31    34.38    34.38      19.33
p2o5perha              68.06    66.32    66.76    73.15      53.17
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 9.992e-03 0.000e+00 1.085e-19     0
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      1.108e+06 2.400e+01 1.408e+04 1.141e+07  8.680e+00
s(Res_wheat_sow).alpha      9.155e-01 0.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.436e+00 9.960e-01 1.101e+00 2.864e+00  1.000e+00
s(District,id='mrf1').tau21 1.339e+07 6.863e+06 1.288e+07 2.309e+07  9.000e+07
s(District,id='mrf1').alpha 9.271e-01 0.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.385e+01 3.267e+01 3.398e+01 3.446e+01  3.486e+01
s(District,id='re2').tau21  2.105e+05 1.509e-04 1.085e+00 2.383e+06  6.468e+01
s(District,id='re2').alpha  9.639e-01 0.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    2.276e+00 1.628e-08 1.449e-01 2.557e+01  9.970e-01
---
Formula sigma1:
---
sigma1 ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + 
    s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                           Mean   2.5%    50%  97.5% parameters
(Intercept)              1.0751 0.2974 1.0842 2.2443     -0.077
rice_duration_class_long 0.1287 0.0769 0.1285 0.1792      0.126
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9867 0.9079 0.9998     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             3.317e-02 7.466e-05 3.889e-03 2.536e-01
s(Res_rice_sow).alpha             9.598e-01 6.580e-01 9.968e-01 1.000e+00
s(Res_rice_sow).edf               1.764e+00 1.009e+00 1.309e+00 4.408e+00
s(g_q5305_irrig_times_rice).tau21 4.623e-01 2.024e-04 2.374e-01 2.072e+00
s(g_q5305_irrig_times_rice).alpha 9.331e-01 6.019e-01 9.934e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   4.691e+00 1.101e+00 5.017e+00 7.258e+00
s(nperha_rice).tau21              5.371e-01 2.471e-04 1.013e-01 3.759e+00
s(nperha_rice).alpha              9.048e-01 3.589e-01 9.916e-01 1.000e+00
s(nperha_rice).edf                3.542e+00 1.027e+00 3.314e+00 7.298e+00
s(p2o5perha_rice).tau21           2.564e-01 1.344e-04 2.828e-02 2.000e+00
s(p2o5perha_rice).alpha           9.355e-01 5.111e-01 9.956e-01 1.000e+00
s(p2o5perha_rice).edf             2.670e+00 1.017e+00 2.307e+00 6.041e+00
s(District,id='mrf1').tau21       6.425e-02 1.278e-04 2.369e-02 3.163e-01
s(District,id='mrf1').alpha       7.059e-01 1.125e-01 7.701e-01 1.000e+00
s(District,id='mrf1').edf         2.778e+01 4.410e+00 3.255e+01 3.455e+01
s(District,id='re2').tau21        7.525e+01 4.238e+01 7.188e+01 1.270e+02
s(District,id='re2').alpha        5.721e-01 5.872e-04 5.661e-01 1.000e+00
s(District,id='re2').edf          3.599e+01 3.599e+01 3.599e+01 3.600e+01
                                  parameters
s(Res_rice_sow).tau21                  0.000
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                    0.872
s(g_q5305_irrig_times_rice).tau21      0.926
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        6.455
s(nperha_rice).tau21                   4.539
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     7.449
s(p2o5perha_rice).tau21                0.948
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  5.386
s(District,id='mrf1').tau21            0.002
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             21.762
s(District,id='re2').tau21         78765.377
s(District,id='re2').alpha                NA
s(District,id='re2').edf              36.000
---
Formula sigma2:
---
sigma2 ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)          6.558e-01 -6.152e-01  7.747e-01  1.840e+00     -0.273
variety_type_NMWV    1.553e-01  1.043e-01  1.549e-01  2.100e-01      0.165
g_q5305_irrig_times  1.081e-01  7.628e-02  1.080e-01  1.390e-01      0.113
nperha              -5.952e-04 -1.272e-03 -5.845e-04  4.729e-05     -0.001
p2o5perha            1.746e-03  4.044e-04  1.742e-03  3.035e-03      0.002
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9022 0.5308 0.9743     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      1.470e-01 3.046e-04 5.700e-02 8.183e-01      0.103
s(Res_wheat_sow).alpha      9.479e-01 6.346e-01 9.985e-01 1.000e+00         NA
s(Res_wheat_sow).edf        2.877e+00 1.023e+00 2.730e+00 5.681e+00      3.237
s(District,id='mrf1').tau21 2.405e-01 3.624e-02 1.989e-01 6.309e-01      0.004
s(District,id='mrf1').alpha 6.189e-01 4.280e-03 6.405e-01 1.000e+00         NA
s(District,id='mrf1').edf   3.423e+01 3.306e+01 3.438e+01 3.475e+01     25.721
s(District,id='re2').tau21  7.422e+01 4.103e+01 7.035e+01 1.301e+02     57.091
s(District,id='re2').alpha  5.778e-01 6.447e-05 5.797e-01 1.000e+00         NA
s(District,id='re2').edf    3.599e+01 3.599e+01 3.599e+01 3.600e+01     35.989
---
Formula rho:
---
rho ~ 1 + s(Res_rice_sow) + s(Res_wheat_sow) + g_q5305_irrig_times_rice + 
    rice_duration_class_long + variety_type_NMWV + s(District, 
    bs = "mrf", xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                              Mean      2.5%       50%     97.5% parameters
(Intercept)               0.224815  0.137230  0.224365  0.317560      0.205
g_q5305_irrig_times_rice -0.003097 -0.018758 -0.002793  0.012400     -0.002
rice_duration_class_long  0.063814 -0.008960  0.063498  0.138752      0.071
variety_type_NMWV         0.014149 -0.062227  0.014157  0.093047      0.010
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9515 0.7365 0.9938     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_rice_sow).tau21       7.137e-02 7.819e-05 3.647e-03 4.979e-01      2.084
s(Res_rice_sow).alpha       9.584e-01 6.980e-01 9.981e-01 1.000e+00         NA
s(Res_rice_sow).edf         1.576e+00 1.004e+00 1.175e+00 3.919e+00      5.833
s(Res_wheat_sow).tau21      2.268e-02 8.280e-05 3.190e-03 1.664e-01      0.000
s(Res_wheat_sow).alpha      9.630e-01 7.190e-01 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.397e+00 1.004e+00 1.141e+00 3.127e+00      0.837
s(District,id='mrf1').tau21 3.252e-03 1.507e-04 2.988e-03 8.202e-03      0.005
s(District,id='mrf1').alpha 8.046e-01 2.629e-01 9.101e-01 1.000e+00         NA
s(District,id='mrf1').edf   1.779e+01 2.870e+00 1.961e+01 2.637e+01     22.875
s(District,id='re2').tau21  7.898e-03 9.088e-05 4.054e-03 3.409e-02      0.000
s(District,id='re2').alpha  8.694e-01 2.547e-01 9.925e-01 1.000e+00         NA
s(District,id='re2').edf    1.243e+01 4.420e-01 1.159e+01 2.747e+01      0.000
---
Sampler summary:
-
DIC = -196139.1 logLik = -97332.91 pd = -390805
runtime = 4143.39
---
Optimizer summary:
-
AICc = 194973.3 edf = 272.5782 logLik = -97196.52
logPost = -3228659 nobs = 4527 runtime = 92.22

par(mfrow = c(2, 3), mar = c(4, 4, 1, 1))
plot(biv_gauss_rev_struct, pages = 1, spar = FALSE, rug = TRUE)

## Prediction
biv_gauss_rev_struct_pred <- predict(biv_gauss_rev_struct, type = "parameter")

biv_gauss_rev_struct_pred= as.data.frame(biv_gauss_rev_struct_pred)

4 Modified Cholesky Decomposition Analyses

4.1 Yield analysis

4.1.1 Trial:Non-structural without controls

# Traditional cholesky
f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_nocntrl<- list(b_grain_yield_ton_per_ha_rice ~ 1 ,
   l_ton_per_hectare ~ 1,
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lambda12 ~ 1)


multivariate_geo_sow_MRF_corr_endo_yld_non_struct_nocntrl <- bamlss(f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_nocntrl, family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat)

AICc 24605.36 logPost -12336.8 logLik -12297.6 edf 5.0000 eps 1.0000 iteration   1
AICc 24596.15 logPost -12332.2 logLik -12293.0 edf 5.0000 eps 0.0502 iteration   2
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0016 iteration   3
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0000 iteration   4
AICc 24596.13 logPost -12332.1 logLik -12293.0 edf 5.0000 eps 0.0000 iteration   4
elapsed time:  0.14sec
Starting the sampler...

|                    |   0% 44.03sec
|*                   |   5% 45.60sec  2.40sec
|**                  |  10% 45.27sec  5.03sec
|***                 |  15% 41.76sec  7.37sec
|****                |  20% 40.48sec 10.12sec
|*****               |  25% 39.60sec 13.20sec
|******              |  30% 37.36sec 16.01sec
|*******             |  35% 35.34sec 19.03sec
|********            |  40% 33.12sec 22.08sec
|*********           |  45% 30.59sec 25.03sec
|**********          |  50% 27.80sec 27.80sec
|***********         |  55% 25.21sec 30.81sec
|************        |  60% 22.56sec 33.84sec
|*************       |  65% 19.85sec 36.86sec
|**************      |  70% 17.09sec 39.87sec
|***************     |  75% 14.20sec 42.61sec
|****************    |  80% 11.37sec 45.48sec
|*****************   |  85%  8.46sec 47.92sec
|******************  |  90%  5.61sec 50.47sec
|******************* |  95%  2.78sec 52.80sec
|********************| 100%  0.00sec 55.11sec

summary(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_nocntrl)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_nocntrl, 
    family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat)
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, lamdiag1 = log, lamdiag2 = log, lambda12 = identity
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 4.010 3.979 4.011 4.042       4.01
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula mu2:
---
l_ton_per_hectare ~ 1
-
Parametric coefficients:
             Mean  2.5%   50% 97.5% parameters
(Intercept) 2.940 2.917 2.940 2.963      2.939
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) -0.09120 -0.11215 -0.09153 -0.06950     -0.091
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9880 0.9031 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.2139 0.1939 0.2138 0.2340      0.214
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9905 0.9191 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) -0.1579 -0.1829 -0.1582 -0.1304     -0.158
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Sampler summary:
-
DIC = 24595.92 logLik = -12295.51 pd = 4.8949
runtime = 55.3
---
Optimizer summary:
-
AICc = 24596.13 edf = 5 logLik = -12293.06
logPost = -12332.19 nobs = 4527 runtime = 0.14

#plot(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_nocntrl)

# 
fitted_values=multivariate_geo_sow_MRF_corr_endo_yld_non_struct_nocntrl$fitted.values

fitted_values=as.data.frame(fitted_values)

summary(fitted_values$lambda12)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.1578 -0.1578 -0.1578 -0.1578 -0.1578 -0.1578 

# Boosted Multivariate
library(gamboostLSS)
library('BayesX')
source('bivariateGaussian.R')
#form = as.formula(cbind(b_grain_yield_ton_per_ha_rice, l_ton_per_hectare) ~ bmrf(bnd = nd))
  
#gam_yields <- gamboostLSS(formula =  form, data = Irrig_Rev_rice_wheat, families = GaussianBV(),control = boost_control(mstop = 1), method = 'noncyclic')
  
#coef.gam_yields <- coef(gam_yields, which = '')

4.1.2 Non-structural

## Non structural ------------------------------------
f_rice_wheat_yield_MRF_corr_endo_yld_non_struct<- list(
  b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lambda12 ~ 1+s(sowdate_fmt_rice_day)+s(sowdate_fmt_wheat_day)+g_q5305_irrig_times_rice+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)


multivariate_geo_sow_MRF_corr_endo_yld_non_struct <- bamlss(f_rice_wheat_yield_MRF_corr_endo_yld_non_struct, type = "modified", family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat)

AICc 21908.98 logPost -11137.0 logLik -10699.4 edf 241.40 eps 1.0000 iteration   1
AICc 20885.84 logPost -10347.2 logLik -10193.3 edf 236.43 eps 0.2391 iteration   2
AICc 20755.27 logPost -10260.9 logLik -10137.2 edf 228.23 eps 0.0598 iteration   3
AICc 20729.83 logPost -10235.4 logLik -10129.0 edf 224.15 eps 0.0232 iteration   4
AICc 20720.97 logPost -10224.0 logLik -10127.5 edf 221.47 eps 0.0065 iteration   5
AICc 20718.62 logPost -10222.1 logLik -10127.2 edf 220.71 eps 0.0032 iteration   6
AICc 20717.90 logPost -10221.9 logLik -10127.1 edf 220.47 eps 0.0024 iteration   7
AICc 20717.47 logPost -10221.7 logLik -10127.1 edf 220.30 eps 0.0015 iteration   8
AICc 20717.16 logPost -10221.5 logLik -10127.0 edf 220.17 eps 0.0010 iteration   9
AICc 20716.91 logPost -10221.4 logLik -10127.0 edf 220.07 eps 0.0008 iteration  10
AICc 20716.72 logPost -10221.2 logLik -10127.0 edf 219.98 eps 0.0009 iteration  11
AICc 20716.56 logPost -10221.1 logLik -10127.0 edf 219.92 eps 0.0006 iteration  12
AICc 20716.44 logPost -10221.0 logLik -10127.0 edf 219.86 eps 0.0005 iteration  13
AICc 20716.33 logPost -10221.0 logLik -10127.0 edf 219.82 eps 0.0004 iteration  14
AICc 20716.25 logPost -10220.9 logLik -10127.0 edf 219.78 eps 0.0004 iteration  15
AICc 20716.18 logPost -10220.9 logLik -10127.0 edf 219.75 eps 0.0003 iteration  16
AICc 20716.12 logPost -10220.8 logLik -10127.0 edf 219.72 eps 0.0003 iteration  17
AICc 20716.07 logPost -10220.8 logLik -10127.0 edf 219.70 eps 0.0004 iteration  18
AICc 20716.03 logPost -10220.8 logLik -10127.0 edf 219.68 eps 0.0005 iteration  19
AICc 20715.99 logPost -10220.7 logLik -10127.0 edf 219.67 eps 0.0008 iteration  20
AICc 20715.97 logPost -10220.7 logLik -10127.0 edf 219.66 eps 0.0001 iteration  21
AICc 20715.94 logPost -10220.7 logLik -10127.0 edf 219.65 eps 0.0003 iteration  22
AICc 20715.92 logPost -10220.7 logLik -10127.0 edf 219.64 eps 0.0001 iteration  23
AICc 20715.91 logPost -10220.7 logLik -10127.0 edf 219.63 eps 0.0000 iteration  24
AICc 20715.91 logPost -10220.7 logLik -10127.0 edf 219.63 eps 0.0000 iteration  24
elapsed time: 36.28sec
Starting the sampler...

|                    |   0%  5.02min
|*                   |   5%  4.48min 14.14sec
|**                  |  10%  5.39min 35.96sec
|***                 |  15%  5.46min 57.86sec
|****                |  20%  5.44min  1.36min
|*****               |  25%  4.88min  1.63min
|******              |  30%  4.47min  1.91min
|*******             |  35%  4.32min  2.33min
|********            |  40%  4.04min  2.70min
|*********           |  45%  3.67min  3.00min
|**********          |  50%  3.20min  3.20min
|***********         |  55%  2.80min  3.42min
|************        |  60%  2.91min  4.36min
|*************       |  65%  2.86min  5.31min
|**************      |  70%  2.69min  6.27min
|***************     |  75%  2.41min  7.24min
|****************    |  80%  2.05min  8.20min
|*****************   |  85%  1.57min  8.91min
|******************  |  90%  1.01min  9.09min
|******************* |  95% 29.33sec  9.29min
|********************| 100%  0.00sec  9.49min

summary(multivariate_geo_sow_MRF_corr_endo_yld_non_struct)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_yld_non_struct, 
    family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat, 
    type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, lamdiag1 = log, lamdiag2 = log, lambda12 = identity
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              1.96309 0.45520 1.61749 3.96395      0.002
rice_duration_class_long 0.09319 0.02537 0.09261 0.15903      0.090
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     8.346e-01 8.321e-02 4.187e-01 4.183e+00
s(sowdate_fmt_rice_day).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       4.182e+00 2.570e+00 3.999e+00 6.418e+00
s(g_q5305_irrig_times_rice).tau21 1.983e+00 2.093e-01 1.329e+00 7.508e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.245e+00 4.365e+00 6.272e+00 7.849e+00
s(nperha_rice).tau21              6.721e-01 1.584e-04 2.366e-01 3.712e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                3.596e+00 1.010e+00 3.565e+00 6.643e+00
s(p2o5perha_rice).tau21           2.761e-01 3.747e-04 8.044e-02 1.752e+00
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             2.786e+00 1.028e+00 2.638e+00 5.481e+00
s(District,id='mrf1').tau21       2.876e-03 9.036e-05 1.890e-03 1.049e-02
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         1.639e+01 2.207e+00 1.781e+01 2.856e+01
s(District,id='re2').tau21        5.518e+00 1.617e-01 5.067e+00 1.498e+01
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.551e+01 3.369e+01 3.581e+01 3.593e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.238
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            3.511
s(g_q5305_irrig_times_rice).tau21      1.888
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        6.647
s(nperha_rice).tau21                   1.414
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     5.525
s(p2o5perha_rice).tau21                0.155
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  3.162
s(District,id='mrf1').tau21            0.029
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             31.822
s(District,id='re2').tau21            11.350
s(District,id='re2').alpha                NA
s(District,id='re2').edf              35.912
---
Formula mu2:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -0.7609677 -1.1836393 -0.6694340 -0.4907862     -1.380
variety_type_NMWV    0.2862040  0.2425258  0.2857962  0.3290698      0.279
g_q5305_irrig_times  0.4228768  0.3962962  0.4230964  0.4498655      0.421
nperha               0.0015015  0.0009101  0.0015045  0.0021319      0.001
p2o5perha            0.0025310  0.0014187  0.0025445  0.0036419      0.003
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 1.058e-02 5.516e-05 1.190e-03 9.240e-02
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.453e+00 1.009e+00 1.177e+00 3.396e+00
s(District,id='mrf1').tau21    9.281e-03 3.260e-04 7.190e-03 3.052e-02
s(District,id='mrf1').alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf      2.782e+01 1.104e+01 3.031e+01 3.321e+01
s(District,id='re2').tau21     5.488e+00 3.066e+00 5.176e+00 9.482e+00
s(District,id='re2').alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf       3.591e+01 3.586e+01 3.591e+01 3.595e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21      0.000
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        1.039
s(District,id='mrf1').tau21         0.004
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf          27.445
s(District,id='re2').tau21          6.063
s(District,id='re2').alpha             NA
s(District,id='re2').edf           35.928
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.06561 0.04368 0.06574 0.08558      0.073
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9907 0.9136 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.5170 0.4963 0.5170 0.5385      0.527
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9900 0.9039 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1 + s(sowdate_fmt_rice_day) + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times_rice + rice_duration_class_long + variety_type_NMWV + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)              -1.827e-01 -2.749e-01 -1.825e-01 -9.466e-02     -0.011
g_q5305_irrig_times_rice  3.294e-04 -1.355e-02  2.523e-05  1.537e-02      0.000
rice_duration_class_long -3.353e-02 -1.069e-01 -3.331e-02  4.333e-02     -0.023
variety_type_NMWV        -6.947e-02 -1.521e-01 -6.879e-02  3.365e-03     -0.048
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21  8.394e-01 2.114e-04 3.208e-01 4.426e+00
s(sowdate_fmt_rice_day).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf    3.292e+00 1.009e+00 3.347e+00 5.949e+00
s(sowdate_fmt_wheat_day).tau21 4.888e-02 9.717e-05 4.160e-03 3.013e-01
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.512e+00 1.005e+00 1.202e+00 3.456e+00
s(District,id='mrf1').tau21    2.557e-03 7.475e-05 2.261e-03 7.716e-03
s(District,id='mrf1').alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf      1.483e+01 1.431e+00 1.624e+01 2.475e+01
s(District,id='re2').tau21     8.281e-03 3.599e-04 5.982e-03 2.849e-02
s(District,id='re2').alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf       1.314e+01 1.364e+00 1.355e+01 2.576e+01
                               parameters
s(sowdate_fmt_rice_day).tau21       1.890
s(sowdate_fmt_rice_day).alpha          NA
s(sowdate_fmt_rice_day).edf         5.054
s(sowdate_fmt_wheat_day).tau21     35.487
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        8.006
s(District,id='mrf1').tau21         0.003
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf          17.374
s(District,id='re2').tau21          0.027
s(District,id='re2').alpha             NA
s(District,id='re2').edf           25.210
---
Sampler summary:
-
DIC = 20550.78 logLik = -10210.04 pd = 130.697
runtime = 570.88
---
Optimizer summary:
-
AICc = 20715.91 edf = 219.6356 logLik = -10127.07
logPost = -10220.71 nobs = 4527 runtime = 36.28

plot(multivariate_geo_sow_MRF_corr_endo_yld_non_struct)

Rice_sow_date_pred <- data.frame("sowdate_fmt_rice_day" = seq(min(Irrig_Rev_rice_wheat$sowdate_fmt_rice_day), max(Irrig_Rev_rice_wheat$sowdate_fmt_rice_day), length = 95))

Rice_sow_date_pred$pCI <- predict(multivariate_geo_sow_MRF_corr_endo_yld_non_struct, newdata = Rice_sow_date_pred, model = "mu1", term = "sowdate_fmt_rice_day",
  FUN = c95, intercept = FALSE)


ylim <- range(c(Rice_sow_date_pred$pCI))

png(file="figures/sowing_rice_plot_unstruct.png",
width=350, height=250)

bamlss::plot2d(pCI ~ sowdate_fmt_rice_day, data = Rice_sow_date_pred, ylim = ylim,xlab="Rice transplanting date", lwd = c(1,3,1),col.lines = "#2E9FDF")

dev.off()

png 
  2 

## Structural --------------------------------------

### First stage ------------------------------------------
# Rice first stage
f_sow_rice_1st_stage <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re")
)

f_sow_rice_1st_stage_MRF <- bamlss(f_sow_rice_1st_stage, data = Irrig_Rev_rice_wheat, family = "gaussian")

AICc 38862.03 logPost -165306. logLik -19371.2 edf 59.010 eps 0.1226 iteration   1
AICc 34841.08 logPost -31072.7 logLik -17339.3 edf 79.788 eps 0.0980 iteration   2
AICc 33498.94 logPost -18399.0 logLik -16648.2 edf 98.970 eps 0.0632 iteration   3
AICc 33180.98 logPost -17093.4 logLik -16491.0 edf 97.287 eps 0.0297 iteration   4
AICc 33096.83 logPost -16986.5 logLik -16452.6 edf 93.751 eps 0.0069 iteration   5
AICc 33056.53 logPost -16935.2 logLik -16435.7 edf 90.674 eps 0.0017 iteration   6
AICc 33040.37 logPost -16899.0 logLik -16429.8 edf 88.587 eps 0.0009 iteration   7
AICc 33035.63 logPost -16869.0 logLik -16428.1 edf 87.868 eps 0.0003 iteration   8
AICc 33028.91 logPost -16845.9 logLik -16427.6 edf 85.110 eps 0.0001 iteration   9
AICc 33028.60 logPost -16840.2 logLik -16427.5 edf 85.077 eps 0.0000 iteration  10
AICc 33028.60 logPost -16840.2 logLik -16427.5 edf 85.077 eps 0.0000 iteration  10
elapsed time:  5.25sec
Starting the sampler...

|                    |   0%  1.57min
|*                   |   5%  1.44min  4.54sec
|**                  |  10%  1.31min  8.70sec
|***                 |  15%  1.20min 12.68sec
|****                |  20%  1.10min 16.56sec
|*****               |  25%  1.02min 20.45sec
|******              |  30% 56.84sec 24.36sec
|*******             |  35% 52.32sec 28.17sec
|********            |  40% 48.33sec 32.22sec
|*********           |  45% 44.11sec 36.09sec
|**********          |  50% 40.12sec 40.12sec
|***********         |  55% 35.98sec 43.98sec
|************        |  60% 31.71sec 47.56sec
|*************       |  65% 27.28sec 50.67sec
|**************      |  70% 23.02sec 53.72sec
|***************     |  75% 18.90sec 56.70sec
|****************    |  80% 14.89sec 59.58sec
|*****************   |  85% 11.01sec  1.04min
|******************  |  90%  7.25sec  1.09min
|******************* |  95%  3.59sec  1.14min
|********************| 100%  0.00sec  1.19min

fitted_f_sow_rice_1st_stage_MRF <- f_sow_rice_1st_stage_MRF$fitted

Irrig_Rev_rice_wheat$Res_rice_sow <- Irrig_Rev_rice_wheat$sowdate_fmt_rice_day - fitted_f_sow_rice_1st_stage_MRF$mu

# Wheat first stage
f_sow_wheat_1st_stage <- list(
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(gw_2018) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re")
)

f_sow_wheat_1st_stage_MRF <- bamlss(f_sow_wheat_1st_stage, data = Irrig_Rev_rice_wheat, family = "gaussian")

AICc 49188.65 logPost -488850. logLik -24543.4 edf 50.285 eps 0.2566 iteration   1
AICc 44824.42 logPost -64385.9 logLik -22386.0 edf 26.046 eps 0.0753 iteration   2
AICc 40409.05 logPost -24539.6 logLik -20136.0 edf 67.444 eps 0.0824 iteration   3
AICc 36648.46 logPost -18973.1 logLik -18246.6 edf 76.219 eps 0.0789 iteration   4
AICc 33900.77 logPost -17313.2 logLik -16871.9 edf 77.104 eps 0.0796 iteration   5
AICc 32636.01 logPost -16736.4 logLik -16238.1 edf 78.490 eps 0.0660 iteration   6
AICc 32419.72 logPost -16629.9 logLik -16129.2 edf 79.163 eps 0.0324 iteration   7
AICc 32413.31 logPost -16627.4 logLik -16125.7 edf 79.502 eps 0.0056 iteration   8
AICc 32412.92 logPost -16627.3 logLik -16125.4 edf 79.574 eps 0.0001 iteration   9
AICc 32412.79 logPost -16627.2 logLik -16125.3 edf 79.581 eps 0.0000 iteration  10
AICc 32412.79 logPost -16627.2 logLik -16125.3 edf 79.581 eps 0.0000 iteration  10
elapsed time:  3.10sec
Starting the sampler...

|                    |   0% 55.93sec
|*                   |   5% 53.77sec  2.83sec
|**                  |  10% 50.94sec  5.66sec
|***                 |  15% 48.05sec  8.48sec
|****                |  20% 46.88sec 11.72sec
|*****               |  25% 44.16sec 14.72sec
|******              |  30% 41.37sec 17.73sec
|*******             |  35% 38.37sec 20.66sec
|********            |  40% 35.67sec 23.78sec
|*********           |  45% 33.10sec 27.08sec
|**********          |  50% 30.41sec 30.41sec
|***********         |  55% 27.34sec 33.42sec
|************        |  60% 24.27sec 36.41sec
|*************       |  65% 21.32sec 39.59sec
|**************      |  70% 18.42sec 42.98sec
|***************     |  75% 15.34sec 46.03sec
|****************    |  80% 12.27sec 49.09sec
|*****************   |  85%  9.24sec 52.36sec
|******************  |  90%  6.16sec 55.47sec
|******************* |  95%  3.08sec 58.55sec
|********************| 100%  0.00sec  1.03min

fitted_f_sow_wheat_1st_stage_MRF <- f_sow_wheat_1st_stage_MRF$fitted

Irrig_Rev_rice_wheat$Res_wheat_sow <- Irrig_Rev_rice_wheat$sowdate_fmt_wheat_day - fitted_f_sow_wheat_1st_stage_MRF$mu


# Multivariate with sowing dates as endogenous ---------------------
f_rice_wheat_yield_MRF_corr_endo <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lamdiag3 ~ 1,
  lamdiag4 ~ 1,
  lambda12 ~ 1,
  lambda13 ~ 1,
  lambda14 ~ 1,
  lambda23 ~ 1,
  lambda24 ~ 1+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lambda34 ~ 1
)

multivariate_geo_sow_MRF_corr_endo <- bamlss(f_rice_wheat_yield_MRF_corr_endo, type = "modified", family = mvnchol_bamlss(k = 4), data = Irrig_Rev_rice_wheat)

AICc 349476.1 logPost -2543606 logLik -174262. edf 430.14 eps 1.0000 iteration   1
AICc 157743.5 logPost -2447306 logLik -78382.3 edf 441.55 eps 0.1825 iteration   2
AICc 104307.5 logPost -2420173 logLik -51667.3 edf 439.10 eps 0.2070 iteration   3
AICc 89316.74 logPost -2412636 logLik -44189.9 edf 424.43 eps 0.1254 iteration   4
AICc 86452.65 logPost -2411216 logLik -42768.9 edf 415.34 eps 0.0628 iteration   5
AICc 86231.98 logPost -2411101 logLik -42661.9 edf 412.53 eps 0.0202 iteration   6
AICc 86215.73 logPost -2411097 logLik -42659.1 edf 408.13 eps 0.0027 iteration   7
AICc 86213.14 logPost -2411094 logLik -42658.2 edf 407.83 eps 0.0007 iteration   8
AICc 86211.64 logPost -2411092 logLik -42657.7 edf 407.62 eps 0.0003 iteration   9
AICc 86210.65 logPost -2411090 logLik -42657.4 edf 407.43 eps 0.0002 iteration  10
AICc 86205.44 logPost -2411208 logLik -42657.3 edf 405.37 eps 0.0001 iteration  11
AICc 86205.08 logPost -2411207 logLik -42657.3 edf 405.26 eps 0.0001 iteration  12
AICc 86202.45 logPost -2412410 logLik -42657.2 edf 404.20 eps 0.0001 iteration  13
AICc 86202.37 logPost -2412333 logLik -42657.2 edf 404.18 eps 0.0001 iteration  14
AICc 86202.37 logPost -2412333 logLik -42657.2 edf 404.18 eps 0.0001 iteration  14
elapsed time:  1.54min
Starting the sampler...

|                    |   0% 11.96min
|*                   |   5% 14.44min 45.59sec
|**                  |  10% 11.77min  1.31min
|***                 |  15% 15.27min  2.69min
|****                |  20% 20.96min  5.24min
|*****               |  25% 20.41min  6.80min
|******              |  30% 17.39min  7.45min
|*******             |  35% 14.97min  8.06min
|********            |  40% 13.11min  8.74min
|*********           |  45% 11.49min  9.40min
|**********          |  50% 10.34min 10.34min
|***********         |  55%  9.01min 11.02min
|************        |  60%  7.91min 11.86min
|*************       |  65%  6.80min 12.64min
|**************      |  70%  5.76min 13.44min
|***************     |  75%  5.04min 15.12min
|****************    |  80%  4.46min 17.84min
|*****************   |  85%  3.32min 18.82min
|******************  |  90%  2.16min 19.40min
|******************* |  95%  1.05min 20.00min
|********************| 100%  0.00sec 20.61min

summary(multivariate_geo_sow_MRF_corr_endo)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo, family = mvnchol_bamlss(k = 4), 
    data = Irrig_Rev_rice_wheat, type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, mu3 = identity, mu4 = identity, lamdiag1 = log, lamdiag2 = log, lamdiag3 = log, lamdiag4 = log, lambda12 = identity, lambda13 = identity, lambda14 = identity, lambda23 = identity, lambda24 = identity, lambda34 = identity
*---
Formula mu1:
---
sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + 
    s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + 
    s(sd_onset_82_15) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                           Mean   2.5%    50%  97.5% parameters
(Intercept)              73.604 71.238 73.658 75.926      2.030
rice_duration_class_long -1.347 -1.979 -1.357 -0.661     -1.341
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(gw_2017).tau21            9.372e+00 7.272e-05 2.628e-01 8.423e+01    428.875
s(gw_2017).alpha            1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(gw_2017).edf              1.750e+00 9.976e-01 1.169e+00 4.717e+00      7.459
s(onset_2017).tau21         5.743e+00 2.132e-04 9.880e-02 5.672e+01   3370.676
s(onset_2017).alpha         1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(onset_2017).edf           1.645e+00 9.994e-01 1.116e+00 4.444e+00      8.245
s(monsoon_onset_dev).tau21  4.636e+00 2.826e-04 2.049e-01 3.705e+01     16.446
s(monsoon_onset_dev).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(monsoon_onset_dev).edf    1.850e+00 9.998e-01 1.260e+00 4.474e+00      3.687
s(median_onset_82_15).tau21 3.208e+01 1.401e-03 5.164e+00 2.075e+02     18.779
s(median_onset_82_15).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(median_onset_82_15).edf   2.907e+00 1.002e+00 2.701e+00 6.253e+00      3.766
s(sd_onset_82_15).tau21     1.044e+01 1.975e-04 8.949e-01 8.812e+01      0.537
s(sd_onset_82_15).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(sd_onset_82_15).edf       1.986e+00 9.993e-01 1.534e+00 5.012e+00      1.379
s(District,id='mrf1').tau21 8.126e+01 3.739e+01 7.534e+01 1.567e+02   1484.377
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.465e+01 3.441e+01 3.466e+01 3.482e+01     34.979
s(District,id='re2').tau21  1.536e+04 9.560e+03 1.473e+04 2.486e+04      1.087
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.599e+01 3.599e+01 3.599e+01 3.600e+01     35.240
---
Formula mu2:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              1.38698 0.50872 1.24165 2.78826      0.000
rice_duration_class_long 0.10034 0.03751 0.09988 0.16397      0.096
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             3.517e+00 1.262e-01 1.788e+00 1.785e+01
s(Res_rice_sow).alpha             1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Res_rice_sow).edf               5.821e+00 3.031e+00 5.908e+00 8.210e+00
s(g_q5305_irrig_times_rice).tau21 1.624e+00 2.184e-01 1.259e+00 5.534e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.141e+00 4.386e+00 6.207e+00 7.607e+00
s(nperha_rice).tau21              8.801e-01 2.617e-02 4.763e-01 4.398e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                4.250e+00 1.885e+00 4.262e+00 6.834e+00
s(p2o5perha_rice).tau21           5.323e-02 8.684e-05 1.376e-03 3.326e-01
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             1.485e+00 1.006e+00 1.095e+00 3.796e+00
s(District,id='mrf1').tau21       3.205e-03 6.981e-05 1.361e-03 1.651e-02
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         1.538e+01 1.777e+00 1.519e+01 3.039e+01
s(District,id='re2').tau21        7.498e+00 1.438e+00 7.290e+00 1.543e+01
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.582e+01 3.546e+01 3.586e+01 3.594e+01
                                  parameters
s(Res_rice_sow).tau21                 16.244
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                    8.170
s(g_q5305_irrig_times_rice).tau21      1.698
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        6.538
s(nperha_rice).tau21                   0.991
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     5.103
s(p2o5perha_rice).tau21                0.172
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  3.239
s(District,id='mrf1').tau21            0.035
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             32.259
s(District,id='re2').tau21             8.948
s(District,id='re2').alpha                NA
s(District,id='re2').edf              35.894
---
Formula mu3:
---
sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                     Mean    2.5%     50%   97.5% parameters
(Intercept)       120.923 113.864 121.663 123.890      3.830
variety_type_NMWV  -3.052  -3.679  -3.047  -2.408     -3.073
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 1.0000 0.9999 1.0000     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(harvest_day_rice).tau21     234.939    43.557   158.344   785.369   1035.210
s(harvest_day_rice).alpha       1.000     1.000     1.000     1.000         NA
s(harvest_day_rice).edf         5.928     4.402     5.881     7.615      8.391
s(District,id='mrf1').tau21    87.154    42.239    80.423   170.282   4326.837
s(District,id='mrf1').alpha     1.000     1.000     1.000     1.000         NA
s(District,id='mrf1').edf      34.779    34.645    34.786    34.876     34.994
s(District,id='re2').tau21  48029.885 29063.260 45581.366 77870.821      1.087
s(District,id='re2').alpha      1.000     1.000     1.000     1.000         NA
s(District,id='re2').edf       35.998    35.997    35.998    35.999     35.240
---
Formula mu4:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -0.4198420 -0.8690868 -0.4939736  0.0935699     -1.419
variety_type_NMWV    0.3437228  0.2907770  0.3432796  0.4000766      0.337
g_q5305_irrig_times  0.4231877  0.3961360  0.4232760  0.4488093      0.424
nperha               0.0015190  0.0009139  0.0015213  0.0021163      0.002
p2o5perha            0.0025913  0.0014752  0.0025751  0.0037039      0.002
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      1.448e-02 8.411e-05 2.479e-03 8.321e-02      0.238
s(Res_wheat_sow).alpha      1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.593e+00 1.012e+00 1.289e+00 3.306e+00      4.795
s(District,id='mrf1').tau21 2.634e-03 4.990e-05 1.616e-03 1.018e-02      0.010
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   2.009e+01 2.724e+00 2.258e+01 3.129e+01     31.282
s(District,id='re2').tau21  4.002e+00 1.734e+00 3.826e+00 7.178e+00      5.082
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.588e+01 3.577e+01 3.589e+01 3.594e+01     35.915
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.216 -2.236 -2.215 -2.196     -2.207
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9897 0.9196 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.06678 0.04526 0.06695 0.08760      0.074
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9896 0.9086 1.0000     1
---
Formula lamdiag3:
---
lamdiag3 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.146 -2.166 -2.146 -2.127     -2.141
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9919 0.9355 1.0000     1
---
Formula lamdiag4:
---
lamdiag4 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.5174 0.4963 0.5170 0.5383      0.527
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9909 0.9191 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1
-
Parametric coefficients:
                  Mean       2.5%        50%      97.5% parameters
(Intercept)  0.0006281 -0.0176094  0.0002021  0.0229855     -0.004
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda13:
---
lambda13 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.007528 0.004159 0.007478 0.011218      0.008
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda14:
---
lambda14 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.008813 0.003627 0.008735 0.014006      0.011
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda23:
---
lambda23 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept)  0.023454 -0.007558  0.023582  0.054381      0.027
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda24:
---
lambda24 ~ 1 + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) -0.2338 -0.2854 -0.2326 -0.1859     -0.036
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(District,id='mrf1').tau21 3.171e-03 2.145e-04 2.913e-03 8.067e-03      0.005
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   1.682e+01 3.579e+00 1.817e+01 2.515e+01     22.153
s(District,id='re2').tau21  8.488e-03 2.603e-04 6.545e-03 2.800e-02      0.024
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    1.374e+01 1.040e+00 1.438e+01 2.567e+01     24.454
---
Formula lambda34:
---
lambda34 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) -0.07259 -0.14164 -0.05666 -0.02145     -0.009
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Sampler summary:
-
DIC = 85813.55 logLik = -42796.32 pd = 220.9055
runtime = 1239.12
---
Optimizer summary:
-
AICc = 86202.37 edf = 404.1805 logLik = -42657.27
logPost = -2412333 nobs = 4527 runtime = 92.58

plot(multivariate_geo_sow_MRF_corr_endo)

## More results -------------------------------
nd <- data.frame("District" = unique(Irrig_Rev_rice_wheat$District))

# Focusing on the cross-equation correlations

## Predict for the structured spatial effects.
p_str_multivariate_geo_sow_MRF_corr_endo_rice_y <- predict(multivariate_geo_sow_MRF_corr_endo, newdata = nd, term = "s(District,id='mrf1')", intercept = FALSE)
p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt <- as.data.frame(p_str_multivariate_geo_sow_MRF_corr_endo_rice_y)
write.csv(p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt, "tables/p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt2.csv")

## And the unstructured spatial effect.
p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y <- predict(multivariate_geo_sow_MRF_corr_endo, newdata = nd, term = "s(District,id='re2')", intercept = FALSE)

# Rice sowing spatial equation

plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y$mu1, id = nd$District, main = expression(mu(rice_sowing)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y$mu1, id = nd$District, main = expression(mu(rice_sowing)), title = "Unstructured spatial effect")

# Rice yield spatial equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y$mu2, id = nd$District, main = expression(mu(rice_yield)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y$mu2, id = nd$District, main = expression(mu(rice_yield)), title = "Unstructured spatial effect")

# Wheat sowing equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y$mu3, id = nd$District, main = expression(mu(wheat_sowing)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y$mu3, id = nd$District, main = expression(mu(wheat_sowing)), title = "Unstructured spatial effect")

# Wheat yield spatial equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y$mu4, id = nd$District, main = expression(mu(wheat_yield)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y$mu4, id = nd$District, main = expression(mu(wheat_yield)), title = "Unstructured spatial effect")

# Focusing on the cross-equation correlations

## MRF smooth effect.
plotmap(India_aoi_sp_bnd,
        x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y$lambda24, id = nd$District,
        main = expression(lambda(rice, wheat)), title = "Structured spatial effect"
)

## Random effects.
plotmap(India_aoi_sp_bnd,
        x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y$lambda24, id = nd$District, main = expression(lambda(rice, wheat)), title = "Unstructured spatial effect"
)

# Rice sowing equation : Non-linear relationships
# s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15)
plot(multivariate_geo_sow_MRF_corr_endo, model = "mu1", term = "s(gw_2017)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu1", term = "s(onset_2017)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu1", term = "s(monsoon_onset_dev)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu1", term = "s(median_onset_82_15)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu1", term = "s(sd_onset_82_15)")

# Rice yield equation
# s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice)

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu2", term = "s(Res_rice_sow)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu2", term = "s(g_q5305_irrig_times_rice)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu2", term = "s(nperha_rice)")

plot(multivariate_geo_sow_MRF_corr_endo, model = "mu2", term = "s(p2o5perha_rice)")

# Wheat sowing equation
# s(harvest_day_rice) + s(gw_2018)
plot(multivariate_geo_sow_MRF_corr_endo, model = "mu3", term = "s(harvest_day_rice)")

# (multivariate_geo_sow_MRF_corr_endo, model = "mu3", term = "s(gw_2018)")

# Wheat yield equation
plot(multivariate_geo_sow_MRF_corr_endo, model = "mu4", term = "s(Res_wheat_sow)")

# Fitted values
multivariate_geo_sow_MRF_corr_endo_fitted_values <- multivariate_geo_sow_MRF_corr_endo$fitted

multivariate_geo_sow_MRF_corr_endo_fitted_values <- as.data.frame(multivariate_geo_sow_MRF_corr_endo_fitted_values)

# Merge the fitted results to the data and export

Irrig_Rev_rice_wheat_Mult_Res <- cbind(Irrig_Rev_rice_wheat, multivariate_geo_sow_MRF_corr_endo_fitted_values)

write.csv(Irrig_Rev_rice_wheat_Mult_Res, "tables/Irrig_Rev_rice_wheat_Mult_Res.csv")

summary(lm(sowdate_fmt_rice_day ~ mu1, Irrig_Rev_rice_wheat_Mult_Res))

Call:
lm(formula = sowdate_fmt_rice_day ~ mu1, data = Irrig_Rev_rice_wheat_Mult_Res)

Residuals:
    Min      1Q  Median      3Q     Max 
-44.574  -5.397  -0.269   4.986  44.985 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.03383    3.41385   -0.01    0.992    
mu1          1.00018    0.01771   56.48   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.093 on 4525 degrees of freedom
Multiple R-squared:  0.4135,    Adjusted R-squared:  0.4134 
F-statistic:  3190 on 1 and 4525 DF,  p-value: < 2.2e-16

summary(lm(b_grain_yield_ton_per_ha_rice ~ l_ton_per_hectare, Irrig_Rev_rice_wheat_Mult_Res))

Call:
lm(formula = b_grain_yield_ton_per_ha_rice ~ l_ton_per_hectare, 
    data = Irrig_Rev_rice_wheat_Mult_Res)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2891 -0.7976 -0.0052  0.7454  3.3894 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        3.34109    0.05974   55.93   <2e-16 ***
l_ton_per_hectare  0.22766    0.01958   11.63   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.08 on 4525 degrees of freedom
Multiple R-squared:  0.02901,   Adjusted R-squared:  0.0288 
F-statistic: 135.2 on 1 and 4525 DF,  p-value: < 2.2e-16

plot((lm(sowdate_fmt_rice_day ~ mu1, Irrig_Rev_rice_wheat_Mult_Res)))

Irrig_Rev_rice_wheat_Mult_Res_sp <- Irrig_Rev_rice_wheat_Mult_Res
coordinates(Irrig_Rev_rice_wheat_Mult_Res_sp) <- c("o_largest_plot_gps_longitude", "o_largest_plot_gps_latitude")

# Map the correlations
library(modelsummary)
Irrig_Rev_rice_wheat_Mult_Res_dist <- datasummary(Heading("District") * District ~ Heading("N obs") * N + Heading("%") * Percent() + lambda24 * (Mean + SD), data = Irrig_Rev_rice_wheat_Mult_Res, output = "data.frame")

library(dplyr)
Irrig_Rev_rice_wheat_Mult_Res_dist <- rename(Irrig_Rev_rice_wheat_Mult_Res_dist, "Mean_Rice_Wheat_Rho" = "Mean")
Irrig_Rev_rice_wheat_Mult_Res_dist <- rename(Irrig_Rev_rice_wheat_Mult_Res_dist, "SD_Rice_Wheat_Rho" = "SD")

Irrig_Rev_rice_wheat_Mult_Res_dist <- subset(Irrig_Rev_rice_wheat_Mult_Res_dist, Irrig_Rev_rice_wheat_Mult_Res_dist$District != "Purnia")


# Bihar and EUP map
# India district Map

library(geodata)

India <- gadm(country = "IND", level = 2, path = "shp")

plot(India)

India_aoi <- subset(India, India$NAME_1 == "Bihar" | India$NAME_2 %in% c("Ballia", "Chandauli", "Deoria", "Ghazipur", "Kushinagar", "Maharajganj", "Mau", "Siddharth Nagar", "Gorakhpur"))

plot(India_aoi)

plot(India_aoi, add = TRUE)

library(sf)

India_aoi_sf <- st_as_sf(India_aoi)
library(mapview)

mapview(India_aoi_sf)

# Dissolve the district polygons to form new polygon of Bihar and EUP
library(sf)
India_aoi_sf_dis <- st_union(India_aoi_sf)
mapview(India_aoi_sf_dis)

###
library(modelsummary)

India_aoi_sf$District <- India_aoi_sf$NAME_2

India_aoi_sf$District[India_aoi_sf$District == "Purba Champaran"] <- "EastChamparan"
India_aoi_sf$District[India_aoi_sf$District == "Pashchim Champaran"] <- "WestChamparan"
India_aoi_sf$District[India_aoi_sf$District == "Bhojpur"] <- "Arah"
India_aoi_sf$District[India_aoi_sf$District == "Ballia"] <- "Balia"
India_aoi_sf$District[India_aoi_sf$District == "Ghazipur"] <- "Gazipur"
India_aoi_sf$District[India_aoi_sf$District == "Siddharth Nagar"] <- "Siddharthnagar"

rice_wheat_yield_rho_dist_sf <- merge(India_aoi_sf, Irrig_Rev_rice_wheat_Mult_Res_dist, by = "District")

rice_wheat_yield_rho_dist_sf$Mean_Rice_Wheat_Rho <- as.numeric(rice_wheat_yield_rho_dist_sf$Mean_Rice_Wheat_Rho)
library(mapview)
mapview(rice_wheat_yield_rho_dist_sf, zcol = "Mean_Rice_Wheat_Rho", layer.name = "Rice wheat equation correlation")

library(sf)
rice_wheat_yield_rho_dist_sf_sp <- as_Spatial(rice_wheat_yield_rho_dist_sf)
library(tmap)
tmap_mode("plot")
rice_wheat_yield_rho_dist_sf_sp_map <- tm_shape(rice_wheat_yield_rho_dist_sf_sp) +
  tm_polygons(col = "Mean_Rice_Wheat_Rho", title = "Rice wheat equation correlation",style="quantile",palette = "YlGn") +
  tm_layout(legend.outside = TRUE)

rice_wheat_yield_rho_dist_sf_sp_map

tmap_save(rice_wheat_yield_rho_dist_sf_sp_map, "figures/rice_wheat_yield_rho_dist_sf_sp_map .png")

5 Revenue analysis

5.0.1 Non structural

# Revenue analysis -----------------------------------------------
### Non structural ---------------------------------
f_rice_wheat_yield_MRF_corr_endo_rev_non_struct<- list(
  revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lambda12 ~ 1+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re")
)


multivariate_geo_sow_MRF_corr_endo_rev_non_struct <- bamlss(f_rice_wheat_yield_MRF_corr_endo_rev_non_struct, type = "modified", family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat)

AICc 57157830 logPost -3552646 logLik -2857891 edf 258.39 eps 1.0000 iteration   1
AICc 20218095 logPost -1687547 logLik -1010904 edf 263.39 eps 0.4249 iteration   2
AICc 74016152 logPost -4320756 logLik -3700807 edf 266.00 eps 0.2429 iteration   3
AICc 27649687 logPost -1443949 logLik -1382484 edf 267.30 eps 0.2409 iteration   4
AICc 10339301 logPost -5231139 logLik -5169650 edf 267.71 eps 0.2074 iteration   5
AICc 38719904 logPost -1942222 logLik -1935994 edf 267.92 eps 0.2407 iteration   6
AICc 14507914 logPost -7262550 logLik -7253954 edf 267.94 eps 0.1969 iteration   7
AICc 54497423 logPost -2727238 logLik -2724868 edf 267.96 eps 0.2428 iteration   8
AICc 20420328 logPost -1025376 logLik -1021013 edf 267.92 eps 0.1584 iteration   9
AICc 76665931 logPost -3857186 logLik -3833268 edf 267.96 eps 0.1866 iteration  10
AICc 28860727 logPost -1446365 logLik -1443007 edf 267.99 eps 0.1669 iteration  11
AICc 10931008 logPost -5488075 logLik -5465219 edf 267.99 eps 0.1552 iteration  12
AICc 4200246. logPost -2113931 logLik -2099838 edf 267.98 eps 0.1524 iteration  13
AICc 1675358. logPost -847210. logLik -837394. edf 267.96 eps 0.1500 iteration  14
AICc 731053.7 logPost -372331. logLik -365242. edf 267.91 eps 0.1474 iteration  15
AICc 381035.8 logPost -195605. logLik -190233. edf 267.79 eps 0.1440 iteration  16
AICc 254456.1 logPost -131232. logLik -126943. edf 267.47 eps 0.1383 iteration  17
AICc 211585.7 logPost -109108. logLik -105509. edf 267.00 eps 0.1269 iteration  18
AICc 199328.4 logPost -102533. logLik -99381.6 edf 265.92 eps 0.1038 iteration  19
AICc 197013.0 logPost -101079. logLik -98224.4 edf 265.48 eps 0.0651 iteration  20
AICc 196834.0 logPost -100804. logLik -98135.5 edf 264.94 eps 0.0239 iteration  21
AICc 196828.3 logPost -100760. logLik -98134.0 edf 263.68 eps 0.0044 iteration  22
AICc 196828.0 logPost -100761. logLik -98134.0 edf 263.59 eps 0.0002 iteration  23
AICc 196828.0 logPost -100768. logLik -98134.0 edf 263.59 eps 0.0001 iteration  24
AICc 196828.0 logPost -100768. logLik -98134.0 edf 263.59 eps 0.0001 iteration  24
elapsed time: 39.13sec
Starting the sampler...

|                    |   0%  4.98min
|*                   |   5%  5.72min 18.05sec
|**                  |  10%  6.24min 41.58sec
|***                 |  15%  6.73min  1.19min
|****                |  20%  6.87min  1.72min
|*****               |  25%  6.97min  2.33min
|******              |  30%  7.54min  3.23min
|*******             |  35%  7.67min  4.13min
|********            |  40%  7.55min  5.03min
|*********           |  45%  7.27min  5.95min
|**********          |  50%  6.84min  6.84min
|***********         |  55%  5.89min  7.19min
|************        |  60%  4.91min  7.37min
|*************       |  65%  4.06min  7.54min
|**************      |  70%  3.30min  7.70min
|***************     |  75%  2.63min  7.88min
|****************    |  80%  2.02min  8.07min
|*****************   |  85%  1.47min  8.31min
|******************  |  90% 56.64sec  8.50min
|******************* |  95% 27.37sec  8.67min
|********************| 100%  0.00sec  8.84min

summary(multivariate_geo_sow_MRF_corr_endo_rev_non_struct)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_rev_non_struct, 
    family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat, 
    type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, lamdiag1 = log, lamdiag2 = log, lambda12 = identity
*---
Formula mu1:
---
revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)               228.942 -648.424  239.757 1118.699     -33.89
rice_duration_class_long  883.320   -6.313  872.974 1760.078    1145.68
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.8657 0.3123 0.9837     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     2.871e+08 6.388e+07 1.977e+08 9.540e+08
s(sowdate_fmt_rice_day).alpha     9.954e-01 9.649e-01 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       4.984e+00 3.859e+00 4.882e+00 6.483e+00
s(g_q5305_irrig_times_rice).tau21 3.356e+08 4.638e+07 2.243e+08 1.365e+09
s(g_q5305_irrig_times_rice).alpha 9.946e-01 9.661e-01 9.997e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.065e+00 4.542e+00 6.062e+00 7.700e+00
s(nperha_rice).tau21              1.027e+08 1.864e+00 1.406e+07 7.870e+08
s(nperha_rice).alpha              9.954e-01 9.527e-01 1.000e+00 1.000e+00
s(nperha_rice).edf                2.915e+00 1.000e+00 2.574e+00 6.665e+00
s(p2o5perha_rice).tau21           1.590e+09 7.398e+07 8.232e+08 7.544e+09
s(p2o5perha_rice).alpha           9.380e-01 5.682e-01 9.978e-01 1.000e+00
s(p2o5perha_rice).edf             6.358e+00 4.119e+00 6.476e+00 8.292e+00
s(District,id='mrf1').tau21       2.603e+07 1.012e+07 2.326e+07 5.659e+07
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         3.420e+01 3.339e+01 3.426e+01 3.469e+01
s(District,id='re2').tau21        2.563e+09 1.584e+09 2.478e+09 4.107e+09
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.598e+01 3.596e+01 3.598e+01 3.599e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21      2.134e+09
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf        8.639e+00
s(g_q5305_irrig_times_rice).tau21  3.210e+09
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    8.756e+00
s(nperha_rice).tau21               1.451e+09
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 8.361e+00
s(p2o5perha_rice).tau21            5.786e+09
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              8.711e+00
s(District,id='mrf1').tau21        1.319e+07
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          3.374e+01
s(District,id='re2').tau21         2.151e+09
s(District,id='re2').alpha                NA
s(District,id='re2').edf           3.597e+01
---
Formula mu2:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -14269.895 -15634.983 -14516.441 -13351.230  -19691.78
variety_type_NMWV     3623.144   3240.019   3750.143   3917.966    4110.10
g_q5305_irrig_times   4751.569   4559.672   4730.838   5281.107    5446.91
nperha                  12.029      2.424     12.494     22.997      16.49
p2o5perha               52.285     31.592     56.463     70.994      64.70
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 9.494e-03 5.615e-28 7.749e-16 0.006
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 5.719e+05 5.681e+01 3.507e+03 5.184e+06
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.117e+00 9.959e-01 1.002e+00 2.172e+00
s(District,id='mrf1').tau21    9.092e+06 9.136e+05 6.239e+06 2.686e+07
s(District,id='mrf1').alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf      3.203e+01 2.644e+01 3.266e+01 3.409e+01
s(District,id='re2').tau21     1.623e+09 9.867e+08 1.548e+09 2.634e+09
s(District,id='re2').alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf       3.591e+01 3.587e+01 3.591e+01 3.595e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21  4.851e+09
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf    8.998e+00
s(District,id='mrf1').tau21     2.081e+07
s(District,id='mrf1').alpha            NA
s(District,id='mrf1').edf       3.394e+01
s(District,id='re2').tau21      6.151e+08
s(District,id='re2').alpha             NA
s(District,id='re2').edf        3.580e+01
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.605 -9.625 -9.605 -9.585     -9.596
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9913 0.9240 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.250 -9.271 -9.250 -9.230     -9.244
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9895 0.9160 0.9999     1
---
Formula lambda12:
---
lambda12 ~ 1 + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.01789 0.01786 0.01789 0.01791      0.018
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9880 0.9258 0.9996     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(District,id='mrf1').tau21 5.449e+00 3.212e+00 5.276e+00 8.696e+00      22.95
s(District,id='mrf1').alpha 4.047e-01 4.381e-10 2.075e-01 1.000e+00         NA
s(District,id='mrf1').edf   3.500e+01 3.500e+01 3.500e+01 3.500e+01      35.00
s(District,id='re2').tau21  7.075e-03 4.206e-03 6.887e-03 1.076e-02     258.50
s(District,id='re2').alpha  4.105e-01 1.200e-09 2.305e-01 1.000e+00         NA
s(District,id='re2').edf    3.500e+01 3.500e+01 3.500e+01 3.500e+01      35.68
---
Sampler summary:
-
DIC = 196582.6 logLik = -98225.73 pd = 131.1437
runtime = 532.09
---
Optimizer summary:
-
AICc = 196828.1 edf = 263.5948 logLik = -98134.08
logPost = -100768.2 nobs = 4527 runtime = 39.13

plot(multivariate_geo_sow_MRF_corr_endo_rev_non_struct)

5.0.2 Structural

### Structural -----------------------------------
f_rice_wheat_yield_MRF_corr_endo_rev <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lamdiag3 ~ 1,
  lamdiag4 ~ 1,
  lambda12 ~ 1,
  lambda13 ~ 1,
  lambda14 ~ 1,
  lambda23 ~ 1,
  lambda24 ~ +s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lambda34 ~ 1
)

multivariate_geo_sow_MRF_corr_endo_rev <- bamlss(f_rice_wheat_yield_MRF_corr_endo_rev, type = "modified", family = mvnchol_bamlss(k = 4), data = Irrig_Rev_rice_wheat)

AICc 56631943 logPost -3529561 logLik -2831597 edf 454.76 eps 1.0000 iteration   1
AICc 20215442 logPost -1437546 logLik -1010772 edf 471.28 eps 0.6691 iteration   2
AICc 75476458 logPost -4167167 logLik -3773822 edf 473.64 eps 0.3790 iteration   3
AICc 28760290 logPost -1805799 logLik -1438014 edf 474.24 eps 0.8107 iteration   4
AICc 10975073 logPost -9141064 logLik -5487535 edf 474.04 eps 0.2412 iteration   5
AICc 42034530 logPost -5751139 logLik -2101725 edf 474.48 eps 0.2425 iteration   6
AICc 16235546 logPost -4461047 logLik -8117767 edf 474.41 eps 0.2641 iteration   7
AICc 62113696 logPost -3959997 logLik -3105679 edf 474.17 eps 0.2022 iteration   8
AICc 24030761 logPost -3770947 logLik -1201532 edf 473.69 eps 0.3679 iteration   9
AICc 92894291 logPost -3698882 logLik -4644661 edf 473.52 eps 0.2113 iteration  10
AICc 36102689 logPost -3667102 logLik -1805081 edf 474.50 eps 1.9859 iteration  11
AICc 14249974 logPost -3688527 logLik -7124490 edf 447.73 eps 0.2894 iteration  12
AICc 5638093. logPost -3895624 logLik -2818537 edf 457.75 eps 0.1973 iteration  13
AICc 2354599. logPost -4793098 logLik -1176778 edf 467.55 eps 0.2858 iteration  14
AICc 1059126. logPost -897833. logLik -529035. edf 472.42 eps 0.2473 iteration  15
AICc 563634.6 logPost -322166. logLik -281288. edf 473.76 eps 0.2740 iteration  16
AICc 373600.9 logPost -193759. logLik -186272. edf 472.84 eps 0.2270 iteration  17
AICc 302426.3 logPost -155379. logLik -150687. edf 470.88 eps 0.1317 iteration  18
AICc 277398.0 logPost -141807. logLik -138178. edf 466.51 eps 0.1435 iteration  19
AICc 268179.0 logPost -137117. logLik -133577. edf 459.69 eps 0.1679 iteration  20
AICc 263416.0 logPost -134779. logLik -131203. edf 453.98 eps 0.2299 iteration  21
AICc 262519.7 logPost -134264. logLik -130766. edf 445.08 eps 0.0719 iteration  22
AICc 262407.5 logPost -134223. logLik -130722. edf 435.06 eps 0.0243 iteration  23
AICc 262351.5 logPost -134492. logLik -130700. edf 429.87 eps 0.0181 iteration  24
AICc 262323.7 logPost -137146. logLik -130689. edf 427.94 eps 0.0171 iteration  25
AICc 262306.7 logPost -163705. logLik -130682. edf 426.06 eps 0.0176 iteration  26
AICc 262296.8 logPost -427590. logLik -130679. edf 425.19 eps 0.0186 iteration  27
AICc 262290.9 logPost -3056847 logLik -130676. edf 424.74 eps 0.0213 iteration  28
AICc 262286.9 logPost -5632809 logLik -130675. edf 424.33 eps 0.0263 iteration  29
AICc 262284.0 logPost -5623866 logLik -130674. edf 423.97 eps 0.0378 iteration  30
AICc 262282.0 logPost -5612347 logLik -130673. edf 423.68 eps 0.0706 iteration  31
AICc 262280.3 logPost -5603035 logLik -130672. edf 423.46 eps 0.9782 iteration  32
AICc 262278.9 logPost -5595340 logLik -130672. edf 423.32 eps 0.0786 iteration  33
AICc 262277.7 logPost -5588448 logLik -130671. edf 423.19 eps 0.0377 iteration  34
AICc 262276.5 logPost -5581294 logLik -130671. edf 423.08 eps 0.0247 iteration  35
AICc 262275.6 logPost -5575193 logLik -130671. edf 422.99 eps 0.0183 iteration  36
AICc 262274.7 logPost -5569372 logLik -130670. edf 422.92 eps 0.0144 iteration  37
AICc 262273.9 logPost -5562368 logLik -130670. edf 422.87 eps 0.0119 iteration  38
AICc 262273.2 logPost -5556702 logLik -130670. edf 422.84 eps 0.0100 iteration  39
AICc 262272.5 logPost -5551938 logLik -130669. edf 422.81 eps 0.0086 iteration  40
AICc 262271.9 logPost -5546830 logLik -130669. edf 422.78 eps 0.0075 iteration  41
AICc 262271.4 logPost -5541938 logLik -130669. edf 422.76 eps 0.0067 iteration  42
AICc 262270.9 logPost -5537255 logLik -130669. edf 422.73 eps 0.0059 iteration  43
AICc 262270.4 logPost -5532730 logLik -130668. edf 422.70 eps 0.0053 iteration  44
AICc 262269.9 logPost -5528402 logLik -130668. edf 422.68 eps 0.0048 iteration  45
AICc 262269.5 logPost -5524348 logLik -130668. edf 422.65 eps 0.0044 iteration  46
AICc 262269.1 logPost -5520164 logLik -130668. edf 422.62 eps 0.0040 iteration  47
AICc 262268.7 logPost -5516233 logLik -130668. edf 422.60 eps 0.0036 iteration  48
AICc 262268.4 logPost -5512541 logLik -130668. edf 422.57 eps 0.0034 iteration  49
AICc 262268.0 logPost -5508536 logLik -130667. edf 422.55 eps 0.0031 iteration  50
AICc 262267.7 logPost -5505226 logLik -130667. edf 422.52 eps 0.0029 iteration  51
AICc 262267.4 logPost -5501564 logLik -130667. edf 422.49 eps 0.0026 iteration  52
AICc 262267.1 logPost -5498742 logLik -130667. edf 422.46 eps 0.0024 iteration  53
AICc 262266.9 logPost -5495686 logLik -130667. edf 422.44 eps 0.0023 iteration  54
AICc 262266.6 logPost -5492542 logLik -130667. edf 422.41 eps 0.0021 iteration  55
AICc 262266.4 logPost -5489355 logLik -130667. edf 422.39 eps 0.0019 iteration  56
AICc 262266.1 logPost -5486917 logLik -130667. edf 422.36 eps 0.0017 iteration  57
AICc 262265.9 logPost -5484264 logLik -130667. edf 422.34 eps 0.0016 iteration  58
AICc 262265.7 logPost -5481418 logLik -130666. edf 422.31 eps 0.0015 iteration  59
AICc 262265.5 logPost -5478916 logLik -130666. edf 422.29 eps 0.0014 iteration  60
AICc 262265.3 logPost -5476474 logLik -130666. edf 422.27 eps 0.0013 iteration  61
AICc 262265.1 logPost -5473809 logLik -130666. edf 422.24 eps 0.0011 iteration  62
AICc 262264.9 logPost -5472103 logLik -130666. edf 422.22 eps 0.0011 iteration  63
AICc 262264.8 logPost -5469075 logLik -130666. edf 422.19 eps 0.0010 iteration  64
AICc 262264.6 logPost -5467212 logLik -130666. edf 422.17 eps 0.0009 iteration  65
AICc 262264.4 logPost -5465148 logLik -130666. edf 422.15 eps 0.0008 iteration  66
AICc 262264.3 logPost -5463707 logLik -130666. edf 422.12 eps 0.0008 iteration  67
AICc 262264.1 logPost -5461336 logLik -130666. edf 422.10 eps 0.0007 iteration  68
AICc 262264.0 logPost -5459937 logLik -130666. edf 422.08 eps 0.0006 iteration  69
AICc 262263.9 logPost -5457682 logLik -130666. edf 422.05 eps 0.0005 iteration  70
AICc 262263.7 logPost -5456145 logLik -130666. edf 422.03 eps 0.0005 iteration  71
AICc 262263.6 logPost -5454566 logLik -130666. edf 422.01 eps 0.0004 iteration  72
AICc 262263.5 logPost -5453280 logLik -130666. edf 421.98 eps 0.0004 iteration  73
AICc 262263.3 logPost -5451173 logLik -130666. edf 421.96 eps 0.0003 iteration  74
AICc 262263.2 logPost -5449737 logLik -130666. edf 421.94 eps 0.0003 iteration  75
AICc 262263.1 logPost -5448520 logLik -130666. edf 421.92 eps 0.0002 iteration  76
AICc 262263.0 logPost -5447060 logLik -130666. edf 421.90 eps 0.0002 iteration  77
AICc 262262.9 logPost -5446225 logLik -130666. edf 421.87 eps 0.0001 iteration  78
AICc 262262.7 logPost -5444927 logLik -130666. edf 421.85 eps 0.0001 iteration  79
AICc 262262.6 logPost -5443676 logLik -130666. edf 421.83 eps 0.0001 iteration  80
AICc 262262.6 logPost -5443676 logLik -130666. edf 421.83 eps 0.0001 iteration  80
elapsed time: 11.34min
Starting the sampler...

|                    |   0%  9.36min
|*                   |   5% 10.77min 34.01sec
|**                  |  10%  9.33min  1.04min
|***                 |  15%  8.63min  1.52min
|****                |  20%  8.87min  2.22min
|*****               |  25%  9.39min  3.13min
|******              |  30%  8.86min  3.80min
|*******             |  35% 11.72min  6.31min
|********            |  40% 13.33min  8.89min
|*********           |  45% 12.48min 10.21min
|**********          |  50% 10.76min 10.76min
|***********         |  55%  9.26min 11.32min
|************        |  60%  7.93min 11.90min
|*************       |  65%  6.72min 12.49min
|**************      |  70%  5.68min 13.25min
|***************     |  75%  4.74min 14.21min
|****************    |  80%  4.09min 16.37min
|*****************   |  85%  3.35min 18.97min
|******************  |  90%  2.28min 20.53min
|******************* |  95%  1.11min 21.08min
|********************| 100%  0.00sec 21.65min

summary(multivariate_geo_sow_MRF_corr_endo_rev)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_rev, family = mvnchol_bamlss(k = 4), 
    data = Irrig_Rev_rice_wheat, type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, mu3 = identity, mu4 = identity, lamdiag1 = log, lamdiag2 = log, lamdiag3 = log, lamdiag4 = log, lambda12 = identity, lambda13 = identity, lambda14 = identity, lambda23 = identity, lambda24 = identity, lambda34 = identity
*---
Formula mu1:
---
sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + 
    s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + 
    s(sd_onset_82_15) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)               1.5401 -0.8638  1.9022  3.1875      2.307
rice_duration_class_long -1.2379 -1.8877 -1.2399 -0.6134     -1.255
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(gw_2017).tau21            5.405e+00 5.655e-04 1.380e-01 4.254e+01      4.098
s(gw_2017).alpha            1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(gw_2017).edf              1.574e+00 1.000e+00 1.093e+00 4.048e+00      2.178
s(onset_2017).tau21         2.110e+00 1.316e-04 1.314e-02 2.489e+01     36.261
s(onset_2017).alpha         1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(onset_2017).edf           1.365e+00 9.988e-01 1.016e+00 3.660e+00      4.002
s(monsoon_onset_dev).tau21  6.258e+00 3.544e-04 4.573e-01 4.229e+01      0.393
s(monsoon_onset_dev).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(monsoon_onset_dev).edf    1.964e+00 1.000e+00 1.482e+00 4.610e+00      1.435
s(median_onset_82_15).tau21 2.934e+01 4.246e-02 1.067e+01 1.489e+02     27.485
s(median_onset_82_15).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(median_onset_82_15).edf   3.239e+00 1.055e+00 3.267e+00 5.935e+00      4.125
s(sd_onset_82_15).tau21     1.075e+01 1.832e-04 9.496e-01 9.664e+01     17.027
s(sd_onset_82_15).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(sd_onset_82_15).edf       1.927e+00 9.992e-01 1.565e+00 5.086e+00      3.330
s(District,id='mrf1').tau21 3.075e+00 1.405e-02 7.588e-01 1.177e+01   1203.412
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   2.376e+01 3.397e+00 2.698e+01 3.372e+01     34.974
s(District,id='re2').tau21  3.845e+04 2.415e+04 3.705e+04 5.990e+04  14286.609
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.600e+01 3.600e+01 3.600e+01 3.600e+01     35.993
---
Formula mu2:
---
revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                           Mean   2.5%    50%  97.5% parameters
(Intercept)               552.7 -648.7  542.1 1772.4      361.2
rice_duration_class_long  996.1  116.2 1001.9 1926.4     1104.8
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.8528 0.3032 0.9685     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             1.292e+09 2.095e+07 7.684e+08 5.613e+09
s(Res_rice_sow).alpha             1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Res_rice_sow).edf               6.380e+00 2.891e+00 6.809e+00 8.429e+00
s(g_q5305_irrig_times_rice).tau21 2.131e+08 2.803e+07 1.341e+08 7.846e+08
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   5.545e+00 4.036e+00 5.487e+00 7.224e+00
s(nperha_rice).tau21              1.027e+08 5.690e+00 4.358e+06 7.852e+08
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                2.568e+00 9.999e-01 1.901e+00 6.592e+00
s(p2o5perha_rice).tau21           3.455e+09 7.667e+06 2.173e+09 1.464e+10
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             6.753e+00 2.493e+00 7.375e+00 8.584e+00
s(District,id='mrf1').tau21       2.234e+07 3.673e+06 1.948e+07 5.917e+07
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         3.371e+01 3.080e+01 3.412e+01 3.471e+01
s(District,id='re2').tau21        2.583e+09 1.604e+09 2.496e+09 4.150e+09
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.597e+01 3.596e+01 3.598e+01 3.599e+01
                                  parameters
s(Res_rice_sow).tau21              2.973e+09
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                8.066e+00
s(g_q5305_irrig_times_rice).tau21  4.073e+08
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    6.646e+00
s(nperha_rice).tau21               4.807e+08
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 6.091e+00
s(p2o5perha_rice).tau21            7.985e+09
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              8.324e+00
s(District,id='mrf1').tau21        5.866e+06
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          3.233e+01
s(District,id='re2').tau21         1.930e+09
s(District,id='re2').alpha                NA
s(District,id='re2').edf           3.597e+01
---
Formula mu3:
---
sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                    Mean   2.5%    50%  97.5% parameters
(Intercept)        5.231  1.897  5.375  7.936      3.900
variety_type_NMWV -3.307 -3.917 -3.326 -2.656     -3.056
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(harvest_day_rice).tau21   2.127e+02 4.970e+01 1.564e+02 7.569e+02     65.162
s(harvest_day_rice).alpha   1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(harvest_day_rice).edf     5.687e+00 4.380e+00 5.641e+00 7.285e+00      4.559
s(District,id='mrf1').tau21 6.291e-01 5.098e-05 2.335e-02 4.381e+00   4299.467
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   1.178e+01 2.224e-02 5.721e+00 3.283e+01     34.994
s(District,id='re2').tau21  1.164e+05 7.194e+04 1.111e+05 1.920e+05  40113.564
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.600e+01 3.600e+01 3.600e+01 3.600e+01     35.998
---
Formula mu4:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -12277.631 -13978.688 -11947.741 -11789.333  -19806.20
variety_type_NMWV     4009.867   3775.107   3823.185   4926.452    4892.47
g_q5305_irrig_times   5170.495   4920.246   5177.098   5258.716    5474.38
nperha                  10.240      6.321     10.579     15.859      16.21
p2o5perha               43.178     38.786     42.027     52.986      65.23
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 6.197e-03 9.568e-25 1.222e-13 0.001
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      1.278e+06 3.244e+01 3.523e+03 1.205e+07  9.726e+01
s(Res_wheat_sow).alpha      1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.174e+00 9.927e-01 1.002e+00 2.692e+00  9.980e-01
s(District,id='mrf1').tau21 8.334e+05 4.087e-01 2.037e+02 5.291e+06  2.494e+07
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   9.515e+00 8.858e-05 4.414e-02 3.242e+01  3.406e+01
s(District,id='re2').tau21  1.437e+09 9.179e+08 1.383e+09 2.270e+09  5.031e+08
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.590e+01 3.586e+01 3.590e+01 3.594e+01  3.576e+01
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.215 -2.236 -2.215 -2.195     -2.209
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9890 0.8978 0.9999     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.608 -9.628 -9.609 -9.587     -9.599
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9904 0.9072 1.0000     1
---
Formula lamdiag3:
---
lamdiag3 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.144 -2.164 -2.144 -2.123      -2.14
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9902 0.9221 1.0000     1
---
Formula lamdiag4:
---
lamdiag4 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.247 -9.268 -9.246 -9.226      -9.24
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9897 0.9051 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept)  0.013633 -0.005496  0.014408  0.030446       0.01
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda13:
---
lambda13 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.008073 0.004220 0.008054 0.011807      0.008
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda14:
---
lambda14 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.007915 0.002066 0.007961 0.014045      0.009
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda23:
---
lambda23 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept) 3.033e-06 1.073e-06 3.037e-06 4.991e-06          0
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9888 0.9166 0.9998     1
---
Formula lambda24:
---
lambda24 ~ +s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.01735 0.01734 0.01735 0.01737      0.017
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9886 0.9184 0.9997     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(District,id='mrf1').tau21 2.444e-03 1.311e-03 2.280e-03 4.102e-03      0.062
s(District,id='mrf1').alpha 4.008e-01 3.383e-10 2.017e-01 1.000e+00         NA
s(District,id='mrf1').edf   3.500e+01 3.499e+01 3.500e+01 3.500e+01     35.000
s(District,id='re2').tau21  7.232e-03 4.366e-03 6.856e-03 1.190e-02      0.211
s(District,id='re2').alpha  3.846e-01 1.067e-10 2.018e-01 1.000e+00         NA
s(District,id='re2').edf    3.561e+01 3.500e+01 3.569e+01 3.600e+01     35.994
---
Formula lambda34:
---
lambda34 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept) -0.044254 -0.090101 -0.047990  0.003942     -0.015
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Sampler summary:
-
DIC = 260981.9 logLik = -130808.8 pd = -635.7777
runtime = 1300.79
---
Optimizer summary:
-
AICc = 262262.7 edf = 421.8356 logLik = -130666
logPost = -5443677 nobs = 4527 runtime = 680.12

plot(multivariate_geo_sow_MRF_corr_endo_rev)

par(mfrow = c(2, 3), mar = c(4, 4, 1, 1))
plot(multivariate_geo_sow_MRF_corr_endo_rev, pages = 1, spar = FALSE, rug = TRUE)

dev.off()

null device 
          1 

# Maximum autocorrelation
plot(multivariate_geo_sow_MRF_corr_endo_rev, which = "max-acf" , spar = FALSE, lag =200)

dev.off()

null device 
          1 

# Traceplots
#par(mar = c(4, 4, 4, 1))
#plot(multivariate_geo_sow_MRF_corr_endo_rev, which = "samples")
#model = "mu1", term = "(Intercept)"


# 95% Credible Interval for Predictions
p <- predict(multivariate_geo_sow_MRF_corr_endo_rev, type = "parameter", FUN = c95)
p=as.data.frame(p)


## More results -------------------------------
nd <- data.frame("District" = unique(Irrig_Rev_rice_wheat$District))

# Focusing on the cross-equation correlations

## Predict for the structured spatial effects.
p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev <- predict(multivariate_geo_sow_MRF_corr_endo_rev, newdata = nd, term = "s(District,id='mrf1')", intercept = FALSE)

p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt_rev <- as.data.frame(p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev)

#write.csv(p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt_rev, "tables/p_str_multivariate_geo_sow_MRF_corr_endo_rice_ydt2_rev.csv")

## And the unstructured spatial effect.
p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev <- predict(multivariate_geo_sow_MRF_corr_endo_rev, newdata = nd, term = "s(District,id='re2')", intercept = FALSE)

# Rice sowing spatial equation

plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu1, id = nd$District, main = expression(mu(rice_sowing)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu1, id = nd$District, main = expression(mu(rice_sowing)), title = "Unstructured spatial effect")

# Rice yield spatial equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu2, id = nd$District, main = expression(mu(rice_revenues)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu2, id = nd$District, main = expression(mu(rice_revenues)), title = "Unstructured spatial effect")

# Wheat sowing equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu3, id = nd$District, main = expression(mu(wheat_sowing)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu3, id = nd$District, main = expression(mu(wheat_sowing)), title = "Unstructured spatial effect")

# Wheat yield spatial equation
plotmap(India_aoi_sp_bnd, x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu4, id = nd$District, main = expression(mu(wheat_revenues)), title = "Structured spatial effect")

plotmap(India_aoi_sp_bnd, x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$mu4, id = nd$District, main = expression(mu(wheat_revenues)), title = "Unstructured spatial effect")

# Focusing on the cross-equation correlations

## MRF smooth effect.
plotmap(India_aoi_sp_bnd,
        x = p_str_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$lambda24, id = nd$District,
        main = expression(lambda(rice, wheat)), title = "Structured spatial effect"
)

## Random effects.
plotmap(India_aoi_sp_bnd,
        x = p_unstr_multivariate_geo_sow_MRF_corr_endo_rice_y_rev$lambda24, id = nd$District, main = expression(lambda(rice, wheat)), title = "Unstructured spatial effect"
)

# Rice sowing equation : Non-linear relationships
# s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15)
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu1", term = "s(gw_2017)")
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu1", term = "s(onset_2017)")
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu1", term = "s(monsoon_onset_dev)")
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu1", term = "s(median_onset_82_15)")
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu1", term = "s(sd_onset_82_15)")


# Rice yield equation
# s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice)

plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu2", term = "s(Res_rice_sow)")

plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu2", term = "s(g_q5305_irrig_times_rice)")

plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu2", term = "s(nperha_rice)")

plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu2", term = "s(p2o5perha_rice)")

# Wheat sowing equation
# s(harvest_day_rice) + s(gw_2018)
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu3", term = "s(harvest_day_rice)")

# (multivariate_geo_sow_MRF_corr_endo, model = "mu3", term = "s(gw_2018)")

# Wheat yield equation
plot(multivariate_geo_sow_MRF_corr_endo_rev, model = "mu4", term = "s(Res_wheat_sow)")


# Fitted values
multivariate_geo_sow_MRF_corr_endo_fitted_values_rev <- multivariate_geo_sow_MRF_corr_endo_rev$fitted

multivariate_geo_sow_MRF_corr_endo_fitted_values_rev <- as.data.frame(multivariate_geo_sow_MRF_corr_endo_fitted_values_rev)

# Merge the fitted results to the data and export

Irrig_Rev_rice_wheat_Mult_Res_rev <- cbind(Irrig_Rev_rice_wheat, multivariate_geo_sow_MRF_corr_endo_fitted_values_rev)

write.csv(Irrig_Rev_rice_wheat_Mult_Res_rev, "tables/Irrig_Rev_rice_wheat_Mult_Res_rev.csv")

summary(lm(sowdate_fmt_rice_day ~ mu1, Irrig_Rev_rice_wheat_Mult_Res_rev))

Call:
lm(formula = sowdate_fmt_rice_day ~ mu1, data = Irrig_Rev_rice_wheat_Mult_Res_rev)

Residuals:
    Min      1Q  Median      3Q     Max 
-44.437  -5.403  -0.199   5.055  45.186 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.1847     3.4311  -0.054    0.957    
mu1           1.0010     0.0178  56.240   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.109 on 4525 degrees of freedom
Multiple R-squared:  0.4114,    Adjusted R-squared:  0.4113 
F-statistic:  3163 on 1 and 4525 DF,  p-value: < 2.2e-16

summary(lm(revenue_rice ~ revenue_wheat, Irrig_Rev_rice_wheat_Mult_Res_rev))

Call:
lm(formula = revenue_rice ~ revenue_wheat, data = Irrig_Rev_rice_wheat_Mult_Res_rev)

Residuals:
   Min     1Q Median     3Q    Max 
-63505 -12206   -640  11764 193340 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.833e+04  8.220e+02   46.63   <2e-16 ***
revenue_wheat 2.797e-01  1.875e-02   14.92   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 17640 on 4525 degrees of freedom
Multiple R-squared:  0.04687,   Adjusted R-squared:  0.04666 
F-statistic: 222.5 on 1 and 4525 DF,  p-value: < 2.2e-16

# 
#library(flexplot)

#flexplot(revenue_rice ~ revenue_wheat, data=Irrig_Rev_rice_wheat_Mult_Res_rev,method = "lm", se = F)



plot((lm(sowdate_fmt_rice_day ~ mu1, Irrig_Rev_rice_wheat_Mult_Res_rev)))

Irrig_Rev_rice_wheat_Mult_Res_sp_rev <- Irrig_Rev_rice_wheat_Mult_Res_rev
coordinates(Irrig_Rev_rice_wheat_Mult_Res_sp_rev) <- c("o_largest_plot_gps_longitude", "o_largest_plot_gps_latitude")

# Map the correlations
library(modelsummary)
mean_na <- function(x) mean(x, na.rm = TRUE)
sd_na <- function(x) SD(x, na.rm = TRUE)


Irrig_Rev_rice_wheat_Mult_Res_dist_rev <- datasummary(Heading("District") * District ~ Heading("N obs") * N + Heading("%") * Percent() + lambda24 * (Mean + SD), data = Irrig_Rev_rice_wheat_Mult_Res_rev, output = "data.frame")

library(dplyr)
Irrig_Rev_rice_wheat_Mult_Res_dist_rev <- rename(Irrig_Rev_rice_wheat_Mult_Res_dist_rev, "Mean_Rice_Wheat_Rho" = "Mean")
Irrig_Rev_rice_wheat_Mult_Res_dist_rev <- rename(Irrig_Rev_rice_wheat_Mult_Res_dist_rev, "SD_Rice_Wheat_Rho" = "SD")

Irrig_Rev_rice_wheat_Mult_Res_dist_rev <- subset(Irrig_Rev_rice_wheat_Mult_Res_dist_rev, Irrig_Rev_rice_wheat_Mult_Res_dist_rev$District != "Purnia")


# Bihar and EUP map
# India district Map

library(geodata)

India <- gadm(country = "IND", level = 2, path = "shp")

plot(India)

India_aoi <- subset(India, India$NAME_1 == "Bihar" | India$NAME_2 %in% c("Ballia", "Chandauli", "Deoria", "Ghazipur", "Kushinagar", "Maharajganj", "Mau", "Siddharth Nagar", "Gorakhpur"))

plot(India_aoi)

plot(India_aoi, add = TRUE)

library(sf)

India_aoi_sf <- st_as_sf(India_aoi)
library(mapview)

mapview(India_aoi_sf)

# Dissolve the district polygons to form new polygon of Bihar and EUP
library(sf)
India_aoi_sf_dis <- st_union(India_aoi_sf)
mapview(India_aoi_sf_dis)

###
library(modelsummary)

India_aoi_sf$District <- India_aoi_sf$NAME_2

India_aoi_sf$District[India_aoi_sf$District == "Purba Champaran"] <- "EastChamparan"
India_aoi_sf$District[India_aoi_sf$District == "Pashchim Champaran"] <- "WestChamparan"
India_aoi_sf$District[India_aoi_sf$District == "Bhojpur"] <- "Arah"
India_aoi_sf$District[India_aoi_sf$District == "Ballia"] <- "Balia"
India_aoi_sf$District[India_aoi_sf$District == "Ghazipur"] <- "Gazipur"
India_aoi_sf$District[India_aoi_sf$District == "Siddharth Nagar"] <- "Siddharthnagar"

rice_wheat_yield_rho_dist_sf_rev <- merge(India_aoi_sf, Irrig_Rev_rice_wheat_Mult_Res_dist_rev, by = "District")

rice_wheat_yield_rho_dist_sf_rev$Mean_Rice_Wheat_Rho <- as.numeric(rice_wheat_yield_rho_dist_sf_rev$Mean_Rice_Wheat_Rho)

library(mapview)
mapview(rice_wheat_yield_rho_dist_sf_rev, zcol = "Mean_Rice_Wheat_Rho", layer.name = "Rice wheat equation correlation")

library(sf)
rice_wheat_yield_rho_dist_sf_sp_rev <- as_Spatial(rice_wheat_yield_rho_dist_sf_rev)
library(tmap)
tmap_mode("plot")
rice_wheat_yield_rho_dist_sf_sp_map_rev <- tm_shape(rice_wheat_yield_rho_dist_sf_sp_rev) +
  tm_polygons(col = "Mean_Rice_Wheat_Rho", title = "Rice wheat revenue \n equation correlation", style = "quantile",palette = "YlGn") +
  tm_layout(legend.outside = TRUE)

rice_wheat_yield_rho_dist_sf_sp_map_rev

tmap_save(rice_wheat_yield_rho_dist_sf_sp_map, "figures/rice_wheat_yield_rho_dist_sf_sp_map .png")

6 Explaining Correlations

6.1 Explaining yield tradeoffs

### Factors explaining the strength of the correlation ---------------------------

## Explain yield trade offs-----------
# Multivariate with sowing dates as endogenous
f_rice_wheat_yield_MRF_corr_endo_more <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lamdiag3 ~ 1,
  lamdiag4 ~ 1,
  lambda12 ~ 1,
  lambda13 ~ 1,
  lambda14 ~ 1,
  lambda23 ~ 1,
  lambda24 ~ Res_rice_sow+Res_wheat_sow+g_q5305_irrig_times_rice+g_q5305_irrig_times + nperha + p2o5perha+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lambda34 ~ 1
)

multivariate_geo_sow_MRF_corr_endo_more <- bamlss(f_rice_wheat_yield_MRF_corr_endo_more, type = "modified", family = mvnchol_bamlss(k = 4), data = Irrig_Rev_rice_wheat)

AICc 349479.7 logPost -2543660 logLik -174254. edf 438.07 eps 1.0000 iteration   1
AICc 157747.2 logPost -2447359 logLik -78374.6 edf 449.36 eps 0.2134 iteration   2
AICc 104291.0 logPost -2420223 logLik -51661.1 edf 437.46 eps 0.2125 iteration   3
AICc 89320.01 logPost -2412706 logLik -44183.2 edf 431.21 eps 0.1289 iteration   4
AICc 86454.97 logPost -2411274 logLik -42762.2 edf 421.80 eps 0.0642 iteration   5
AICc 86234.44 logPost -2411159 logLik -42655.3 edf 419.05 eps 0.0205 iteration   6
AICc 86218.16 logPost -2411155 logLik -42652.5 edf 414.64 eps 0.0027 iteration   7
AICc 86215.56 logPost -2411152 logLik -42651.5 edf 414.33 eps 0.0007 iteration   8
AICc 86214.05 logPost -2411150 logLik -42651.1 edf 414.11 eps 0.0004 iteration   9
AICc 86213.06 logPost -2411148 logLik -42650.8 edf 413.92 eps 0.0003 iteration  10
AICc 86207.84 logPost -2411265 logLik -42650.7 edf 411.86 eps 0.0002 iteration  11
AICc 86204.98 logPost -2412556 logLik -42650.6 edf 410.72 eps 0.0002 iteration  12
AICc 86204.84 logPost -2412484 logLik -42650.6 edf 410.68 eps 0.0001 iteration  13
AICc 86204.75 logPost -2412404 logLik -42650.6 edf 410.66 eps 0.0001 iteration  14
AICc 86204.67 logPost -2412403 logLik -42650.6 edf 410.63 eps 0.0001 iteration  15
AICc 86204.60 logPost -2412403 logLik -42650.6 edf 410.61 eps 0.0001 iteration  16
AICc 86204.60 logPost -2412403 logLik -42650.6 edf 410.61 eps 0.0001 iteration  16
elapsed time:  1.76min
Starting the sampler...

|                    |   0% 26.44min
|*                   |   5% 18.76min 59.25sec
|**                  |  10% 31.16min  3.46min
|***                 |  15% 32.77min  5.78min
|****                |  20% 31.97min  7.99min
|*****               |  25% 25.76min  8.59min
|******              |  30% 21.43min  9.19min
|*******             |  35% 18.18min  9.79min
|********            |  40% 15.76min 10.51min
|*********           |  45% 13.64min 11.16min
|**********          |  50% 12.13min 12.13min
|***********         |  55% 11.71min 14.32min
|************        |  60% 11.44min 17.16min
|*************       |  65% 10.36min 19.23min
|**************      |  70%  8.49min 19.82min
|***************     |  75%  6.83min 20.50min
|****************    |  80%  5.28min 21.13min
|*****************   |  85%  3.84min 21.76min
|******************  |  90%  2.52min 22.71min
|******************* |  95%  1.23min 23.39min
|********************| 100%  0.00sec 25.44min

summary(multivariate_geo_sow_MRF_corr_endo_more)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_more, family = mvnchol_bamlss(k = 4), 
    data = Irrig_Rev_rice_wheat, type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, mu3 = identity, mu4 = identity, lamdiag1 = log, lamdiag2 = log, lamdiag3 = log, lamdiag4 = log, lambda12 = identity, lambda13 = identity, lambda14 = identity, lambda23 = identity, lambda24 = identity, lambda34 = identity
*---
Formula mu1:
---
sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + 
    s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + 
    s(sd_onset_82_15) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)               5.1814  2.9983  5.1478  7.1299      2.032
rice_duration_class_long -1.3291 -1.9914 -1.3377 -0.6872     -1.343
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(gw_2017).tau21            2.124e+01 3.861e-03 3.845e+00 1.763e+02    424.976
s(gw_2017).alpha            1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(gw_2017).edf              2.377e+00 1.003e+00 2.146e+00 5.616e+00      7.450
s(onset_2017).tau21         7.066e+00 4.289e-04 2.225e-01 5.559e+01   3171.147
s(onset_2017).alpha         1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(onset_2017).edf           1.622e+00 1.000e+00 1.233e+00 4.384e+00      8.212
s(monsoon_onset_dev).tau21  8.948e+00 2.375e-04 6.080e-01 6.301e+01     15.680
s(monsoon_onset_dev).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(monsoon_onset_dev).edf    2.111e+00 9.996e-01 1.583e+00 5.035e+00      3.644
s(median_onset_82_15).tau21 2.288e+01 3.521e-03 2.436e+00 1.677e+02     18.496
s(median_onset_82_15).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(median_onset_82_15).edf   2.619e+00 1.005e+00 2.260e+00 6.010e+00      3.752
s(sd_onset_82_15).tau21     1.625e+01 9.212e-05 5.413e-01 1.130e+02      0.527
s(sd_onset_82_15).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(sd_onset_82_15).edf       2.049e+00 9.981e-01 1.376e+00 5.278e+00      1.374
s(District,id='mrf1').tau21 4.346e+01 2.104e+01 4.109e+01 8.283e+01   1478.441
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.443e+01 3.412e+01 3.445e+01 3.468e+01     34.979
s(District,id='re2').tau21  3.665e+04 2.349e+04 3.544e+04 5.945e+04      1.087
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.600e+01 3.600e+01 3.600e+01 3.600e+01     35.240
---
Formula mu2:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              1.67385 0.23287 1.44645 3.84049      0.000
rice_duration_class_long 0.10018 0.02995 0.10058 0.16271      0.096
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             2.965e+00 6.157e-02 1.259e+00 1.633e+01
s(Res_rice_sow).alpha             1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Res_rice_sow).edf               5.440e+00 2.475e+00 5.489e+00 8.155e+00
s(g_q5305_irrig_times_rice).tau21 1.750e+00 2.367e-01 1.245e+00 5.842e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.146e+00 4.475e+00 6.196e+00 7.635e+00
s(nperha_rice).tau21              8.287e-01 9.097e-03 4.046e-01 4.388e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                4.091e+00 1.440e+00 4.095e+00 6.848e+00
s(p2o5perha_rice).tau21           1.078e-01 7.997e-05 7.140e-03 8.442e-01
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             1.912e+00 1.006e+00 1.409e+00 4.716e+00
s(District,id='mrf1').tau21       4.041e-03 1.630e-04 2.780e-03 1.469e-02
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         1.897e+01 3.752e+00 2.058e+01 2.983e+01
s(District,id='re2').tau21        6.864e+00 1.765e-01 6.645e+00 1.720e+01
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.561e+01 3.382e+01 3.586e+01 3.594e+01
                                  parameters
s(Res_rice_sow).tau21                 16.484
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                    8.181
s(g_q5305_irrig_times_rice).tau21      1.603
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        6.482
s(nperha_rice).tau21                   1.100
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     5.228
s(p2o5perha_rice).tau21                0.164
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  3.212
s(District,id='mrf1').tau21            0.035
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf             32.244
s(District,id='re2').tau21             8.871
s(District,id='re2').alpha                NA
s(District,id='re2').edf              35.895
---
Formula mu3:
---
sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                     Mean    2.5%     50%   97.5% parameters
(Intercept)       116.444 114.702 116.330 118.443      3.830
variety_type_NMWV  -3.068  -3.654  -3.076  -2.475     -3.073
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(harvest_day_rice).tau21     221.464    53.396   158.215   721.773   1035.658
s(harvest_day_rice).alpha       1.000     1.000     1.000     1.000         NA
s(harvest_day_rice).edf         5.996     4.687     5.947     7.450      8.391
s(District,id='mrf1').tau21   115.277    61.002   108.137   215.024   4313.280
s(District,id='mrf1').alpha     1.000     1.000     1.000     1.000         NA
s(District,id='mrf1').edf      34.839    34.699    34.852    34.920     34.994
s(District,id='re2').tau21  49485.358 30985.569 47382.591 77299.629      1.087
s(District,id='re2').alpha      1.000     1.000     1.000     1.000         NA
s(District,id='re2').edf       35.999    35.998    35.999    35.999     35.240
---
Formula mu4:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", 
    xt = list(penalty = K)) + s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -0.3199544 -1.1540389 -0.5010616  0.7835981     -1.418
variety_type_NMWV    0.3440775  0.2940813  0.3428368  0.3955469      0.337
g_q5305_irrig_times  0.4218101  0.3961507  0.4220398  0.4462687      0.424
nperha               0.0015477  0.0009453  0.0015424  0.0021626      0.002
p2o5perha            0.0025582  0.0013766  0.0025677  0.0036979      0.002
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      2.121e-02 8.432e-05 4.942e-03 1.823e-01      0.189
s(Res_wheat_sow).alpha      1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.782e+00 1.011e+00 1.503e+00 4.111e+00      4.537
s(District,id='mrf1').tau21 8.382e-03 1.329e-04 5.810e-03 3.350e-02      0.012
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   2.641e+01 6.010e+00 2.951e+01 3.330e+01     31.791
s(District,id='re2').tau21  3.822e+00 6.081e-01 3.549e+00 8.805e+00      4.189
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.583e+01 3.546e+01 3.588e+01 3.595e+01     35.898
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.215 -2.237 -2.215 -2.196     -2.207
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9919 0.9321 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
               Mean    2.5%     50%   97.5% parameters
(Intercept) 0.06654 0.04767 0.06606 0.08805      0.074
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9904 0.9074 1.0000     1
---
Formula lamdiag3:
---
lamdiag3 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.146 -2.167 -2.146 -2.125     -2.141
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9902 0.9170 0.9999     1
---
Formula lamdiag4:
---
lamdiag4 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) 0.5204 0.4983 0.5204 0.5411      0.528
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9893 0.9150 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept)  0.004189 -0.011292  0.002808  0.029823     -0.004
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda13:
---
lambda13 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.007584 0.003963 0.007600 0.011134      0.008
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda14:
---
lambda14 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.007999 0.001933 0.008187 0.013001      0.011
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda23:
---
lambda23 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept)  0.023309 -0.008724  0.023407  0.054297      0.027
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda24:
---
lambda24 ~ Res_rice_sow + Res_wheat_sow + g_q5305_irrig_times_rice + 
    g_q5305_irrig_times + nperha + p2o5perha + rice_duration_class_long + 
    variety_type_NMWV + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)              -1.346e-01 -3.104e-01 -1.347e-01  2.640e-02      0.046
Res_rice_sow              3.707e-03  3.829e-05  3.784e-03  7.405e-03      0.004
Res_wheat_sow             2.993e-03 -7.858e-04  2.959e-03  6.923e-03      0.003
g_q5305_irrig_times_rice  2.015e-03 -1.330e-02  2.377e-03  1.631e-02      0.000
g_q5305_irrig_times      -1.597e-02 -6.285e-02 -1.619e-02  3.246e-02     -0.021
nperha                    6.682e-04 -3.702e-04  6.751e-04  1.641e-03      0.001
p2o5perha                -1.892e-03 -3.823e-03 -1.919e-03 -3.694e-05     -0.002
rice_duration_class_long -1.992e-02 -9.935e-02 -1.756e-02  5.614e-02     -0.020
variety_type_NMWV        -8.467e-02 -1.568e-01 -8.307e-02 -1.307e-02     -0.062
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(District,id='mrf1').tau21 1.936e-03 6.196e-05 1.544e-03 6.313e-03      0.004
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   1.250e+01 1.198e+00 1.354e+01 2.354e+01     20.340
s(District,id='re2').tau21  1.015e-02 1.411e-04 8.396e-03 3.280e-02      0.024
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    1.462e+01 5.533e-01 1.641e+01 2.683e+01     24.527
---
Formula lambda34:
---
lambda34 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) -0.08395 -0.13195 -0.08099 -0.02795     -0.009
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Sampler summary:
-
DIC = 85812.61 logLik = -42792.31 pd = 228.0025
runtime = 1531.17
---
Optimizer summary:
-
AICc = 86204.61 edf = 410.6116 logLik = -42650.62
logPost = -2412404 nobs = 4527 runtime = 105.8

plot(multivariate_geo_sow_MRF_corr_endo_more)

6.2 Explain economic tradeoffs

f_rice_wheat_yield_MRF_corr_endo_rev_more <- list(
  sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + s(sd_onset_82_15) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + s(District, bs = "mrf", xt = list("penalty" = K)) +
    s(District, bs = "re"),
  revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + nperha + p2o5perha + s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lamdiag1 ~ 1,
  lamdiag2 ~ 1,
  lamdiag3 ~ 1,
  lamdiag4 ~ 1,
  lambda12 ~ 1,
  lambda13 ~ 1,
  lambda14 ~ 1,
  lambda23 ~ 1,
  lambda24 ~ 1+Res_rice_sow+Res_wheat_sow+g_q5305_irrig_times_rice+g_q5305_irrig_times + nperha + p2o5perha+rice_duration_class_long+variety_type_NMWV+s(District, bs = "mrf", xt = list("penalty" = K)) + s(District, bs = "re"),
  lambda34 ~ 1
)

multivariate_geo_sow_MRF_corr_endo_rev_more <- bamlss(f_rice_wheat_yield_MRF_corr_endo_rev_more, type = "modified", family = mvnchol_bamlss(k = 4), data = Irrig_Rev_rice_wheat)

AICc 56535854 logPost -3524756 logLik -2826792 edf 462.76 eps 1.0000 iteration   1
AICc 20170424 logPost -1435293 logLik -1008521 edf 479.29 eps 0.8513 iteration   2
AICc 75618025 logPost -4174075 logLik -3780901 edf 481.61 eps 0.4775 iteration   3
AICc 28799515 logPost -1807622 logLik -1439975 edf 482.21 eps 0.4605 iteration   4
AICc 11043251 logPost -9173803 logLik -5521625 edf 482.03 eps 0.4034 iteration   5
AICc 42237344 logPost -2473896 logLik -2111866 edf 482.55 eps 0.2681 iteration   6
AICc 16230214 logPost -1174283 logLik -8115102 edf 482.17 eps 0.2747 iteration   7
AICc 62829719 logPost -6762797 logLik -3141480 edf 482.23 eps 0.3094 iteration   8
AICc 24171426 logPost -1590689 logLik -1208565 edf 481.51 eps 0.2492 iteration   9
AICc 93639620 logPost -8690497 logLik -4681927 edf 481.30 eps 0.2648 iteration  10
AICc 36486501 logPost -2616072 logLik -1824271 edf 481.51 eps 0.2377 iteration  11
AICc 14498075 logPost -1200979 logLik -7248498 edf 481.80 eps 0.4452 iteration  12
AICc 5717335. logPost -7284075 logLik -2858128 edf 481.93 eps 0.3483 iteration  13
AICc 2366477. logPost -5572464 logLik -1182699 edf 481.92 eps 0.2964 iteration  14
AICc 1073193. logPost -637937. logLik -536056. edf 482.59 eps 0.6669 iteration  15
AICc 569322.1 logPost -382832. logLik -284121. edf 482.25 eps 0.4157 iteration  16
AICc 376211.7 logPost -201966. logLik -187567. edf 481.35 eps 0.4781 iteration  17
AICc 302578.7 logPost -167950. logLik -150753. edf 478.82 eps 0.2081 iteration  18
AICc 276232.5 logPost -145469. logLik -137586. edf 473.94 eps 0.2068 iteration  19
AICc 266108.9 logPost -136417. logLik -132534. edf 465.90 eps 0.2437 iteration  20
AICc 262795.2 logPost -134516. logLik -130885. edf 460.30 eps 0.1929 iteration  21
AICc 262481.3 logPost -134247. logLik -130737. edf 452.34 eps 0.1093 iteration  22
AICc 262385.8 logPost -134151. logLik -130699. edf 444.96 eps 0.1034 iteration  23
AICc 262340.1 logPost -134102. logLik -130680. edf 441.92 eps 0.5443 iteration  24
AICc 262315.7 logPost -134080. logLik -130670. edf 440.18 eps 0.0930 iteration  25
AICc 262298.9 logPost -134077. logLik -130664. edf 438.11 eps 0.0432 iteration  26
AICc 262289.6 logPost -134289. logLik -130660. edf 437.15 eps 0.0276 iteration  27
AICc 262284.1 logPost -136557. logLik -130658. edf 436.65 eps 0.0199 iteration  28
AICc 262280.3 logPost -158976. logLik -130657. edf 436.19 eps 0.0147 iteration  29
AICc 262277.6 logPost -370157. logLik -130656. edf 435.75 eps 0.0120 iteration  30
AICc 262275.3 logPost -2033809 logLik -130655. edf 435.27 eps 0.0117 iteration  31
AICc 262272.6 logPost -1128628 logLik -130655. edf 434.59 eps 0.0080 iteration  32
AICc 262270.7 logPost -2695166 logLik -130655. edf 434.11 eps 0.0070 iteration  33
AICc 262269.4 logPost -8563210 logLik -130654. edf 433.83 eps 0.0059 iteration  34
AICc 262268.7 logPost -1055731 logLik -130654. edf 433.69 eps 0.0056 iteration  35
AICc 262268.1 logPost -1003980 logLik -130654. edf 433.59 eps 0.0047 iteration  36
AICc 262267.6 logPost -9553042 logLik -130654. edf 433.49 eps 0.0043 iteration  37
AICc 262267.0 logPost -9223377 logLik -130654. edf 433.40 eps 0.0019 iteration  38
AICc 262266.5 logPost -8995342 logLik -130653. edf 433.32 eps 0.0016 iteration  39
AICc 262266.0 logPost -8841596 logLik -130653. edf 433.25 eps 0.0014 iteration  40
AICc 262265.7 logPost -8729803 logLik -130653. edf 433.19 eps 0.0014 iteration  41
AICc 262265.4 logPost -8644026 logLik -130653. edf 433.14 eps 0.0012 iteration  42
AICc 262265.1 logPost -8575350 logLik -130653. edf 433.09 eps 0.0011 iteration  43
AICc 262264.8 logPost -8518361 logLik -130653. edf 433.05 eps 0.0009 iteration  44
AICc 262264.6 logPost -8469892 logLik -130653. edf 433.00 eps 0.0012 iteration  45
AICc 262264.4 logPost -8427871 logLik -130653. edf 432.97 eps 0.0009 iteration  46
AICc 262264.2 logPost -8390747 logLik -130653. edf 432.94 eps 0.0007 iteration  47
AICc 262264.1 logPost -8357537 logLik -130653. edf 432.91 eps 0.0006 iteration  48
AICc 262263.9 logPost -8327422 logLik -130653. edf 432.88 eps 0.0006 iteration  49
AICc 262263.7 logPost -8299838 logLik -130653. edf 432.85 eps 0.0005 iteration  50
AICc 262263.5 logPost -8274349 logLik -130653. edf 432.82 eps 0.0005 iteration  51
AICc 262261.0 logPost -8250699 logLik -130653. edf 431.80 eps 0.0006 iteration  52
AICc 262260.6 logPost -8228950 logLik -130652. edf 431.76 eps 0.0006 iteration  53
AICc 262260.2 logPost -8205391 logLik -130652. edf 431.70 eps 0.0007 iteration  54
AICc 262259.8 logPost -8187710 logLik -130652. edf 431.64 eps 0.0006 iteration  55
AICc 262259.6 logPost -8152502 logLik -130652. edf 431.58 eps 0.0005 iteration  56
AICc 262259.4 logPost -8119501 logLik -130652. edf 431.56 eps 0.0004 iteration  57
AICc 262259.3 logPost -8092425 logLik -130652. edf 431.53 eps 0.0004 iteration  58
AICc 262259.1 logPost -8070069 logLik -130652. edf 431.51 eps 0.0003 iteration  59
AICc 262259.0 logPost -8051336 logLik -130652. edf 431.49 eps 0.0003 iteration  60
AICc 262258.9 logPost -8035387 logLik -130652. edf 431.47 eps 0.0002 iteration  61
AICc 262258.8 logPost -8021528 logLik -130652. edf 431.45 eps 0.0002 iteration  62
AICc 262258.7 logPost -8009346 logLik -130652. edf 431.43 eps 0.0002 iteration  63
AICc 262258.6 logPost -7991787 logLik -130652. edf 431.42 eps 0.0014 iteration  64
AICc 262258.5 logPost -7982524 logLik -130652. edf 431.41 eps 0.0001 iteration  65
AICc 262258.5 logPost -7973825 logLik -130652. edf 431.41 eps 0.0002 iteration  66
AICc 262258.5 logPost -7965587 logLik -130652. edf 431.40 eps 0.0001 iteration  67
AICc 262258.5 logPost -7965587 logLik -130652. edf 431.40 eps 0.0001 iteration  67
elapsed time:  8.70min
Starting the sampler...

|                    |   0% 11.80min
|*                   |   5% 35.28min  1.86min
|**                  |  10% 36.34min  4.04min
|***                 |  15% 36.28min  6.40min
|****                |  20% 31.33min  7.83min
|*****               |  25% 25.27min  8.42min
|******              |  30% 21.38min  9.16min
|*******             |  35% 18.12min  9.76min
|********            |  40% 15.55min 10.36min
|*********           |  45% 13.91min 11.38min
|**********          |  50% 14.05min 14.05min
|***********         |  55% 13.73min 16.78min
|************        |  60% 12.47min 18.70min
|*************       |  65% 10.54min 19.58min
|**************      |  70%  8.67min 20.23min
|***************     |  75%  6.95min 20.85min
|****************    |  80%  5.36min 21.45min
|*****************   |  85%  3.91min 22.14min
|******************  |  90%  2.52min 22.70min
|******************* |  95%  1.23min 23.39min
|********************| 100%  0.00sec 23.98min

summary(multivariate_geo_sow_MRF_corr_endo_rev_more)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_rev_more, family = mvnchol_bamlss(k = 4), 
    data = Irrig_Rev_rice_wheat, type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, mu3 = identity, mu4 = identity, lamdiag1 = log, lamdiag2 = log, lamdiag3 = log, lamdiag4 = log, lambda12 = identity, lambda13 = identity, lambda14 = identity, lambda23 = identity, lambda24 = identity, lambda34 = identity
*---
Formula mu1:
---
sowdate_fmt_rice_day ~ 1 + rice_duration_class_long + s(gw_2017) + 
    s(onset_2017) + s(monsoon_onset_dev) + s(median_onset_82_15) + 
    s(sd_onset_82_15) + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              15.4807  6.1063 16.6115 20.0978      2.245
rice_duration_class_long -1.2609 -1.8770 -1.2609 -0.6515     -1.260
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(gw_2017).tau21            1.353e+01 1.502e-04 2.513e+00 1.026e+02      0.000
s(gw_2017).alpha            1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(gw_2017).edf              2.136e+00 9.989e-01 1.910e+00 4.923e+00      0.038
s(onset_2017).tau21         1.068e+00 1.838e-04 1.579e-02 9.277e+00     31.295
s(onset_2017).alpha         1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(onset_2017).edf           1.286e+00 9.992e-01 1.020e+00 2.884e+00      3.858
s(monsoon_onset_dev).tau21  5.246e+00 2.502e-04 1.322e-01 4.384e+01      0.314
s(monsoon_onset_dev).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(monsoon_onset_dev).edf    1.737e+00 9.997e-01 1.179e+00 4.652e+00      1.368
s(median_onset_82_15).tau21 1.062e+01 2.131e-04 7.817e-02 1.045e+02     32.367
s(median_onset_82_15).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(median_onset_82_15).edf   1.929e+00 9.995e-01 1.101e+00 5.509e+00      4.280
s(sd_onset_82_15).tau21     5.885e+00 6.225e-05 9.728e-03 6.399e+01     13.268
s(sd_onset_82_15).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(sd_onset_82_15).edf       1.365e+00 9.973e-01 1.009e+00 4.637e+00      3.120
s(District,id='mrf1').tau21 5.380e+01 1.783e+01 4.871e+01 1.191e+02   1222.087
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.449e+01 3.399e+01 3.452e+01 3.477e+01     34.975
s(District,id='re2').tau21  3.360e+04 2.020e+04 3.229e+04 5.443e+04  14167.022
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.600e+01 3.599e+01 3.600e+01 3.600e+01     35.993
---
Formula mu2:
---
revenue_rice ~ 1 + rice_duration_class_long + s(Res_rice_sow) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)                554.83 -1321.54   541.81  2714.08      547.5
rice_duration_class_long  1068.84    71.27  1090.97  2103.45     1163.1
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.7853 0.2332 0.8888     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(Res_rice_sow).tau21             3.680e+08 1.034e+07 1.377e+08 2.416e+09
s(Res_rice_sow).alpha             1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Res_rice_sow).edf               4.826e+00 2.449e+00 4.657e+00 7.813e+00
s(g_q5305_irrig_times_rice).tau21 2.459e+08 1.996e+07 1.408e+08 1.126e+09
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   5.495e+00 3.624e+00 5.474e+00 7.488e+00
s(nperha_rice).tau21              9.983e+07 5.902e+00 2.500e+06 8.691e+08
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                2.435e+00 9.318e-01 1.567e+00 6.642e+00
s(p2o5perha_rice).tau21           8.674e+08 5.862e+02 3.628e+07 5.567e+09
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             3.924e+00 9.998e-01 3.248e+00 8.055e+00
s(District,id='mrf1').tau21       1.306e+07 2.135e+04 5.032e+06 5.897e+07
s(District,id='mrf1').alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='mrf1').edf         2.762e+01 2.185e+00 3.178e+01 3.466e+01
s(District,id='re2').tau21        2.523e+09 1.605e+09 2.421e+09 4.118e+09
s(District,id='re2').alpha        1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(District,id='re2').edf          3.597e+01 3.590e+01 3.597e+01 3.598e+01
                                  parameters
s(Res_rice_sow).tau21              2.336e+09
s(Res_rice_sow).alpha                     NA
s(Res_rice_sow).edf                7.873e+00
s(g_q5305_irrig_times_rice).tau21  3.213e+08
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    6.389e+00
s(nperha_rice).tau21               3.446e+08
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 5.698e+00
s(p2o5perha_rice).tau21            5.684e+09
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              8.128e+00
s(District,id='mrf1').tau21        5.137e+06
s(District,id='mrf1').alpha               NA
s(District,id='mrf1').edf          3.202e+01
s(District,id='re2').tau21         1.901e+09
s(District,id='re2').alpha                NA
s(District,id='re2').edf           3.597e+01
---
Formula mu3:
---
sowdate_fmt_wheat_day ~ 1 + variety_type_NMWV + s(harvest_day_rice) + 
    s(District, bs = "mrf", xt = list(penalty = K)) + s(District, 
    bs = "re")
-
Parametric coefficients:
                    Mean   2.5%    50%  97.5% parameters
(Intercept)        6.293  0.322  5.992 11.456      3.904
variety_type_NMWV -3.096 -3.789 -3.095 -2.457     -3.057
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(harvest_day_rice).tau21   2.469e+02 4.710e+01 1.662e+02 9.901e+02     65.038
s(harvest_day_rice).alpha   1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(harvest_day_rice).edf     5.696e+00 4.275e+00 5.662e+00 7.453e+00      4.557
s(District,id='mrf1').tau21 5.931e-02 2.002e-04 2.929e-03 3.666e-01   4325.874
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   6.324e+00 6.917e-02 9.627e-01 2.489e+01     34.994
s(District,id='re2').tau21  1.136e+05 7.380e+04 1.101e+05 1.769e+05  39706.382
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.600e+01 3.600e+01 3.600e+01 3.600e+01     35.998
---
Formula mu4:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(Res_wheat_sow) + g_q5305_irrig_times + 
    nperha + p2o5perha + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -1.394e+04 -1.565e+04 -1.325e+04 -1.246e+04  -19861.67
variety_type_NMWV    4.300e+03  3.978e+03  4.277e+03  4.826e+03    4876.68
g_q5305_irrig_times  5.152e+03  4.732e+03  5.164e+03  5.441e+03    5473.31
nperha               6.322e+00  1.388e-01  3.903e+00  1.572e+01      16.31
p2o5perha            5.790e+01  4.497e+01  5.681e+01  7.400e+01      65.30
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 1.411e-02 1.491e-24 3.816e-13 0.026
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(Res_wheat_sow).tau21      5.114e+06 7.255e+01 9.702e+04 4.504e+07  2.422e+08
s(Res_wheat_sow).alpha      1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(Res_wheat_sow).edf        1.449e+00 9.968e-01 1.043e+00 3.876e+00  7.339e+00
s(District,id='mrf1').tau21 3.348e+06 4.435e+05 2.677e+06 9.582e+06  2.395e+07
s(District,id='mrf1').alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='mrf1').edf   3.012e+01 2.210e+01 3.092e+01 3.327e+01  3.404e+01
s(District,id='re2').tau21  1.530e+09 9.119e+08 1.468e+09 2.394e+09  5.059e+08
s(District,id='re2').alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00         NA
s(District,id='re2').edf    3.591e+01 3.586e+01 3.591e+01 3.594e+01  3.576e+01
---
Formula lamdiag1:
---
lamdiag1 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.216 -2.236 -2.215 -2.195     -2.209
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9912 0.9238 1.0000     1
---
Formula lamdiag2:
---
lamdiag2 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.609 -9.630 -9.610 -9.587     -9.599
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9901 0.9110 0.9999     1
---
Formula lamdiag3:
---
lamdiag3 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -2.145 -2.164 -2.144 -2.126      -2.14
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9900 0.9178 1.0000     1
---
Formula lamdiag4:
---
lamdiag4 ~ 1
-
Parametric coefficients:
              Mean   2.5%    50%  97.5% parameters
(Intercept) -9.243 -9.264 -9.243 -9.223     -9.237
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9910 0.9201 1.0000     1
---
Formula lambda12:
---
lambda12 ~ 1
-
Parametric coefficients:
                  Mean       2.5%        50%      97.5% parameters
(Intercept)  0.0128191 -0.0009523  0.0126661  0.0268923      0.007
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda13:
---
lambda13 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.007594 0.004019 0.007566 0.011626      0.008
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda14:
---
lambda14 ~ 1
-
Parametric coefficients:
                Mean     2.5%      50%    97.5% parameters
(Intercept) 0.009157 0.003989 0.009228 0.014008       0.01
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Formula lambda23:
---
lambda23 ~ 1
-
Parametric coefficients:
                 Mean      2.5%       50%     97.5% parameters
(Intercept) 3.138e-06 1.139e-06 3.154e-06 5.169e-06          0
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9878 0.9117 0.9993     1
---
Formula lambda24:
---
lambda24 ~ 1 + Res_rice_sow + Res_wheat_sow + g_q5305_irrig_times_rice + 
    g_q5305_irrig_times + nperha + p2o5perha + rice_duration_class_long + 
    variety_type_NMWV + s(District, bs = "mrf", xt = list(penalty = K)) + 
    s(District, bs = "re")
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)               2.240e-02  2.238e-02  2.241e-02  2.243e-02      0.022
Res_rice_sow              2.365e-07  2.063e-08  2.363e-07  4.714e-07      0.000
Res_wheat_sow             2.887e-07  4.494e-08  2.843e-07  5.440e-07      0.000
g_q5305_irrig_times_rice  2.152e-08 -1.103e-06  1.414e-08  1.108e-06      0.000
g_q5305_irrig_times      -1.981e-06 -4.836e-06 -2.010e-06  1.223e-06      0.000
nperha                   -8.995e-08 -1.575e-07 -8.916e-08 -2.321e-08      0.000
p2o5perha                 4.348e-09 -1.229e-07  1.645e-09  1.387e-07      0.000
rice_duration_class_long -5.153e-06 -9.973e-06 -5.231e-06 -7.559e-07      0.000
variety_type_NMWV        -1.009e-06 -6.964e-06 -8.471e-07  4.419e-06      0.000
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9229 0.5300 0.9917     1
-
Smooth terms:
                                 Mean      2.5%       50%     97.5% parameters
s(District,id='mrf1').tau21 1.903e-03 1.154e-03 1.862e-03 2.966e-03      0.004
s(District,id='mrf1').alpha 4.046e-01 1.493e-10 1.920e-01 1.000e+00         NA
s(District,id='mrf1').edf   3.500e+01 3.500e+01 3.500e+01 3.500e+01     34.998
s(District,id='re2').tau21  8.332e-03 4.986e-03 8.118e-03 1.406e-02      0.001
s(District,id='re2').alpha  3.949e-01 3.668e-10 2.189e-01 1.000e+00         NA
s(District,id='re2').edf    3.599e+01 3.590e+01 3.600e+01 3.600e+01     35.006
---
Formula lambda34:
---
lambda34 ~ 1
-
Parametric coefficients:
                  Mean       2.5%        50%      97.5% parameters
(Intercept)  0.0051358 -0.0472669 -0.0006477  0.0755230     -0.014
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
---
Sampler summary:
-
DIC = 261845.3 logLik = -130805.4 pd = 234.4823
runtime = 1442.36
---
Optimizer summary:
-
AICc = 262258.5 edf = 431.4048 logLik = -130652.3
logPost = -79655879 nobs = 4527 runtime = 521.76

dev.off()

null device 
          1 

plot(multivariate_geo_sow_MRF_corr_endo_rev_more)
dev.off()

null device 
          1 

7 Point referenced geoadditive specification

7.1 Yield analysis

# Point referenced geoadditive specification --------------------

Irrig_Rev_rice_wheat_sp <- SpatialPointsDataFrame(cbind(Irrig_Rev_rice_wheat$Longitude, Irrig_Rev_rice_wheat$Latitude), data = Irrig_Rev_rice_wheat, proj4string = CRS("+proj=longlat +datum=WGS84"))

### Yield analysis --------------------------------------

### Non structural 
f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_pointgeo<- list(
  b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(Longitude,Latitude),
  l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(Longitude,Latitude),
  lamdiag1 ~ 1+rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(Longitude,Latitude),
  lamdiag2 ~ 1+variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(Longitude,Latitude),
  lambda12 ~ 1+Res_rice_sow+Res_wheat_sow+g_q5305_irrig_times_rice+g_q5305_irrig_times + nperha + p2o5perha+rice_duration_class_long+variety_type_NMWV+s(sowdate_fmt_rice_day)+s(sowdate_fmt_wheat_day)+s(Longitude,Latitude)
)


multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo <- bamlss(f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_pointgeo, type = "modified", family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat_sp)

AICc 21163.81 logPost -10718.3 logLik -10389.6 edf 184.34 eps 1.0000 iteration   1
AICc 20564.24 logPost -10410.2 logLik -10077.9 edf 195.29 eps 0.4209 iteration   2
AICc 20457.66 logPost -10370.7 logLik -10020.3 edf 199.22 eps 0.1765 iteration   3
AICc 20434.62 logPost -10361.4 logLik -10008.4 edf 199.64 eps 0.0340 iteration   4
AICc 20429.58 logPost -10359.1 logLik -10005.7 edf 199.77 eps 0.0460 iteration   5
AICc 20428.35 logPost -10358.0 logLik -10005.3 edf 199.58 eps 0.0284 iteration   6
AICc 20428.20 logPost -10358.2 logLik -10005.2 edf 199.64 eps 0.0052 iteration   7
AICc 20428.13 logPost -10358.4 logLik -10005.1 edf 199.68 eps 0.0015 iteration   8
AICc 20428.13 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0011 iteration   9
AICc 20428.12 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0016 iteration  10
AICc 20428.12 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0005 iteration  11
AICc 20428.12 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0003 iteration  12
AICc 20428.12 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0002 iteration  13
AICc 20428.11 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0002 iteration  14
AICc 20428.11 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0001 iteration  15
AICc 20428.11 logPost -10358.4 logLik -10005.1 edf 199.69 eps 0.0001 iteration  16
AICc 20428.11 logPost -10358.4 logLik -10005.0 edf 199.69 eps 0.0001 iteration  17
AICc 20428.11 logPost -10358.4 logLik -10005.0 edf 199.69 eps 0.0001 iteration  17
elapsed time: 53.27sec
Starting the sampler...

|                    |   0%  6.05min
|*                   |   5%  4.67min 14.75sec
|**                  |  10%  4.30min 28.64sec
|***                 |  15%  7.74min  1.37min
|****                |  20%  7.08min  1.77min
|*****               |  25%  6.10min  2.03min
|******              |  30%  5.28min  2.26min
|*******             |  35%  4.94min  2.66min
|********            |  40%  4.70min  3.14min
|*********           |  45%  4.29min  3.51min
|**********          |  50%  3.74min  3.74min
|***********         |  55%  3.33min  4.07min
|************        |  60%  3.03min  4.54min
|*************       |  65%  2.64min  4.90min
|**************      |  70%  2.21min  5.17min
|***************     |  75%  1.80min  5.39min
|****************    |  80%  1.42min  5.69min
|*****************   |  85%  1.07min  6.07min
|******************  |  90% 42.93sec  6.44min
|******************* |  95% 21.11sec  6.68min
|********************| 100%  0.00sec  6.92min

summary(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_yld_non_struct_pointgeo, 
    family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat_sp, 
    type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, lamdiag1 = log, lamdiag2 = log, lambda12 = identity
*---
Formula mu1:
---
b_grain_yield_ton_per_ha_rice ~ 1 + rice_duration_class_long + 
    s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + 
    s(p2o5perha_rice) + s(Longitude, Latitude)
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              3.96264 3.92023 3.96233 4.00193      3.962
rice_duration_class_long 0.09495 0.02873 0.09528 0.15805      0.096
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     7.384e-01 7.159e-02 4.186e-01 3.145e+00
s(sowdate_fmt_rice_day).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       4.198e+00 2.541e+00 4.071e+00 6.237e+00
s(g_q5305_irrig_times_rice).tau21 2.116e+00 1.960e-01 1.475e+00 8.137e+00
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   6.338e+00 4.284e+00 6.410e+00 7.926e+00
s(nperha_rice).tau21              1.825e-01 2.321e-04 3.811e-02 1.168e+00
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                2.373e+00 1.014e+00 2.108e+00 5.247e+00
s(p2o5perha_rice).tau21           3.828e-01 1.693e-04 5.448e-02 2.528e+00
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             2.699e+00 1.012e+00 2.407e+00 5.971e+00
s(Longitude,Latitude).tau21       3.191e+00 1.770e+00 3.005e+00 5.445e+00
s(Longitude,Latitude).alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Longitude,Latitude).edf         2.662e+01 2.539e+01 2.663e+01 2.763e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.316
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            3.856
s(g_q5305_irrig_times_rice).tau21     11.212
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        8.139
s(nperha_rice).tau21                   0.466
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     4.259
s(p2o5perha_rice).tau21                0.201
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  3.512
s(Longitude,Latitude).tau21            2.685
s(Longitude,Latitude).alpha               NA
s(Longitude,Latitude).edf             26.471
---
Formula mu2:
---
l_ton_per_hectare ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(Longitude, Latitude)
-
Parametric coefficients:
                         Mean      2.5%       50%     97.5% parameters
(Intercept)         1.6038340 1.5164863 1.6039620 1.6924453      1.623
variety_type_NMWV   0.2492248 0.2059049 0.2494708 0.2921974      0.246
g_q5305_irrig_times 0.3968414 0.3699816 0.3969940 0.4235952      0.394
nperha              0.0011810 0.0006257 0.0011737 0.0017715      0.001
p2o5perha           0.0029622 0.0019520 0.0029711 0.0039972      0.003
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21  0.037539  0.000115  0.002821  0.338879
s(sowdate_fmt_wheat_day).alpha  1.000000  1.000000  1.000000  1.000000
s(sowdate_fmt_wheat_day).edf    1.900660  1.022620  1.418309  4.810184
s(Longitude,Latitude).tau21     0.940936  0.434484  0.888667  1.682995
s(Longitude,Latitude).alpha     1.000000  1.000000  1.000000  1.000000
s(Longitude,Latitude).edf      25.785633 23.699154 25.890801 27.187335
                               parameters
s(sowdate_fmt_wheat_day).tau21      4.321
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        7.407
s(Longitude,Latitude).tau21         1.775
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf          27.302
---
Formula lamdiag1:
---
lamdiag1 ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(Longitude, Latitude)
-
Parametric coefficients:
                             Mean     2.5%      50%    97.5% parameters
(Intercept)               0.09941  0.06545  0.09920  0.13401      0.111
rice_duration_class_long -0.07134 -0.13318 -0.06969 -0.01674     -0.070
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9768 0.8320 1.0000     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     2.723e-02 7.334e-05 2.758e-03 2.586e-01
s(sowdate_fmt_rice_day).alpha     9.716e-01 7.194e-01 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       1.596e+00 1.007e+00 1.222e+00 3.989e+00
s(g_q5305_irrig_times_rice).tau21 1.314e-01 2.340e-04 6.681e-02 5.641e-01
s(g_q5305_irrig_times_rice).alpha 9.349e-01 5.239e-01 9.975e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   3.583e+00 1.113e+00 3.764e+00 5.897e+00
s(nperha_rice).tau21              8.951e-02 1.506e-04 2.182e-02 6.882e-01
s(nperha_rice).alpha              9.517e-01 5.852e-01 9.992e-01 1.000e+00
s(nperha_rice).edf                2.285e+00 1.016e+00 2.050e+00 5.105e+00
s(p2o5perha_rice).tau21           3.291e-01 1.071e-04 6.914e-03 3.350e+00
s(p2o5perha_rice).alpha           9.401e-01 3.451e-01 9.991e-01 1.000e+00
s(p2o5perha_rice).edf             2.226e+00 1.012e+00 1.536e+00 6.624e+00
s(Longitude,Latitude).tau21       7.347e-01 3.369e-01 6.953e-01 1.259e+00
s(Longitude,Latitude).alpha       6.346e-01 6.824e-02 6.508e-01 1.000e+00
s(Longitude,Latitude).edf         2.379e+01 2.096e+01 2.390e+01 2.573e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.014
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            1.816
s(g_q5305_irrig_times_rice).tau21      0.121
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        4.307
s(nperha_rice).tau21                   0.011
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     1.723
s(p2o5perha_rice).tau21                2.786
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  6.431
s(Longitude,Latitude).tau21            0.703
s(Longitude,Latitude).alpha               NA
s(Longitude,Latitude).edf             23.941
---
Formula lamdiag2:
---
lamdiag2 ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(Longitude, Latitude)
-
Parametric coefficients:
                         Mean      2.5%       50%     97.5% parameters
(Intercept)          0.815882  0.707948  0.816239  0.920627      0.852
variety_type_NMWV   -0.185989 -0.239146 -0.185140 -0.133166     -0.186
g_q5305_irrig_times -0.103428 -0.135355 -0.102959 -0.071912     -0.111
nperha               0.001300  0.000616  0.001301  0.001968      0.001
p2o5perha           -0.002260 -0.003528 -0.002268 -0.001074     -0.002
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9454 0.6666 0.9980     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 8.760e-02 1.014e-04 9.359e-03 6.865e-01
s(sowdate_fmt_wheat_day).alpha 9.491e-01 5.028e-01 9.990e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   2.119e+00 1.012e+00 1.688e+00 5.023e+00
s(Longitude,Latitude).tau21    3.995e-01 1.614e-01 3.701e-01 8.289e-01
s(Longitude,Latitude).alpha    6.866e-01 1.351e-01 7.141e-01 1.000e+00
s(Longitude,Latitude).edf      2.138e+01 1.765e+01 2.147e+01 2.460e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21      0.021
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        1.986
s(Longitude,Latitude).tau21         0.732
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf          24.209
---
Formula lambda12:
---
lambda12 ~ 1 + Res_rice_sow + Res_wheat_sow + g_q5305_irrig_times_rice + 
    g_q5305_irrig_times + nperha + p2o5perha + rice_duration_class_long + 
    variety_type_NMWV + s(sowdate_fmt_rice_day) + s(sowdate_fmt_wheat_day) + 
    s(Longitude, Latitude)
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)              -1.934e-01 -3.666e-01 -1.924e-01 -3.144e-02     -0.219
Res_rice_sow              7.749e-03 -7.739e-04  7.534e-03  1.690e-02      0.000
Res_wheat_sow            -3.890e-03 -1.400e-02 -3.969e-03  6.188e-03     -0.001
g_q5305_irrig_times_rice -4.463e-03 -1.897e-02 -4.448e-03  9.559e-03     -0.005
g_q5305_irrig_times       9.287e-03 -3.618e-02  8.862e-03  5.572e-02      0.007
nperha                    5.797e-04 -3.643e-04  5.695e-04  1.614e-03      0.001
p2o5perha                -1.858e-03 -3.619e-03 -1.905e-03 -4.828e-05     -0.002
rice_duration_class_long -2.906e-02 -1.074e-01 -2.766e-02  4.863e-02     -0.023
variety_type_NMWV        -3.057e-02 -1.037e-01 -3.026e-02  5.122e-02     -0.021
-
Acceptance probability:
      Mean 2.5% 50% 97.5%
alpha    1    1   1     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21  2.823e-01 1.374e-04 3.406e-02 2.353e+00
s(sowdate_fmt_rice_day).alpha  1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf    2.224e+00 1.006e+00 1.796e+00 5.273e+00
s(sowdate_fmt_wheat_day).tau21 2.134e-01 1.596e-04 2.039e-02 1.864e+00
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   2.071e+00 1.009e+00 1.698e+00 5.315e+00
s(Longitude,Latitude).tau21    1.214e-01 8.399e-03 9.265e-02 3.950e-01
s(Longitude,Latitude).alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Longitude,Latitude).edf      1.126e+01 4.482e+00 1.123e+01 1.780e+01
                               parameters
s(sowdate_fmt_rice_day).tau21       0.236
s(sowdate_fmt_rice_day).alpha          NA
s(sowdate_fmt_rice_day).edf         3.077
s(sowdate_fmt_wheat_day).tau21     83.378
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        8.448
s(Longitude,Latitude).tau21         0.611
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf          19.812
---
Sampler summary:
-
DIC = 20448.74 logLik = -10138.11 pd = 172.5218
runtime = 416.06
---
Optimizer summary:
-
AICc = 20428.12 edf = 199.6951 logLik = -10005.1
logPost = -10358.48 nobs = 4527 runtime = 53.27

dev.off()

null device 
          1 

plot(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo)
dev.off()

null device 
          1 

multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo_fitted=multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo$fitted.values

multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo_fitted=as.data.frame(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo_fitted)

Irrig_Rev_rice_wheat_sp$yield_non_struct_lambda12 <- predict(multivariate_geo_sow_MRF_corr_endo_yld_non_struct_pointgeo,model = "lambda12")

library(tmap)
tmap_mode("plot")
tm_shape(Irrig_Rev_rice_wheat_sp) +
  tm_dots(col = "yield_non_struct_lambda12", title = "Rice-wheat yield equation \n correlation parameter", 
          style = "quantile",palette = "-Spectral",
          size = 0.5) +
  tm_layout(legend.outside = TRUE)+
  tm_legend(text.size = 1)  

7.2 Revenue analysis

# Revenue analysis -----------------------------------------------

### Non structural ---------------------------------

f_rice_wheat_yield_MRF_corr_endo_rev_non_struct_pointgeo<- list(
  revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(Longitude,Latitude),
  revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(Longitude,Latitude),
  lamdiag1 ~ 1+rice_duration_class_long + s(sowdate_fmt_rice_day) + s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + s(Longitude,Latitude),
  lamdiag2 ~ 1+variety_type_NMWV + s(sowdate_fmt_wheat_day) + g_q5305_irrig_times + nperha + p2o5perha + s(Longitude,Latitude),
  lambda12 ~ 1+g_q5305_irrig_times_rice+g_q5305_irrig_times + nperha + p2o5perha+rice_duration_class_long+variety_type_NMWV+s(sowdate_fmt_rice_day)+s(sowdate_fmt_wheat_day)+s(Longitude,Latitude)
)


multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo <- bamlss(f_rice_wheat_yield_MRF_corr_endo_rev_non_struct_pointgeo, type = "modified", family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat_sp)

AICc 67950871 logPost -3457542 logLik -3397543 edf 260.82 eps 1.0000 iteration   1
AICc 23018311 logPost -1157492 logLik -1150915 edf 270.53 eps 1.3817 iteration   2
AICc 84628983 logPost -4238272 logLik -4231449 edf 272.93 eps 0.6104 iteration   3
AICc 31616001 logPost -1581467 logLik -1580800 edf 273.70 eps 0.3555 iteration   4
AICc 11888008 logPost -5944674 logLik -5944003 edf 273.91 eps 0.6701 iteration   5
AICc 44784440 logPost -2239292 logLik -2239221 edf 273.97 eps 0.3096 iteration   6
AICc 16899252 logPost -8449723 logLik -8449623 edf 273.99 eps 0.3830 iteration   7
AICc 63922172 logPost -3196147 logLik -3196105 edf 273.99 eps 0.3560 iteration   8
AICc 24274044 logPost -1213737 logLik -1213699 edf 273.99 eps 0.4854 iteration   9
AICc 92779134 logPost -4639313 logLik -4638927 edf 273.99 eps 0.2912 iteration  10
AICc 35838692 logPost -1792298 logLik -1791905 edf 273.99 eps 0.2908 iteration  11
AICc 14083488 logPost -7045446 logLik -7041452 edf 273.99 eps 0.7237 iteration  12
AICc 5689626. logPost -2848571 logLik -2844521 edf 273.99 eps 0.2424 iteration  13
AICc 2404975. logPost -1206238 logLik -1202195 edf 273.97 eps 0.3528 iteration  14
AICc 1096477. logPost -551985. logLik -547946. edf 273.93 eps 0.3607 iteration  15
AICc 564877.6 logPost -286203. logLik -282147. edf 273.80 eps 0.3686 iteration  16
AICc 345788.3 logPost -176648. logLik -172603. edf 273.50 eps 0.4955 iteration  17
AICc 255574.0 logPost -131525. logLik -127496. edf 272.67 eps 0.2934 iteration  18
AICc 219369.5 logPost -113389. logLik -109396. edf 270.68 eps 0.1861 iteration  19
AICc 205392.8 logPost -106368. logLik -102412. edf 267.11 eps 0.1626 iteration  20
AICc 199876.5 logPost -103579. logLik -99659.0 edf 262.88 eps 0.1841 iteration  21
AICc 197480.1 logPost -102350. logLik -98465.6 edf 258.64 eps 0.3085 iteration  22
AICc 196366.1 logPost -101764. logLik -97914.2 edf 253.67 eps 0.4418 iteration  23
AICc 195877.4 logPost -101550. logLik -97671.8 edf 252.01 eps 8.8334 iteration  24
AICc 195641.7 logPost -101783. logLik -97556.2 edf 249.98 eps 1.1581 iteration  25
AICc 195533.3 logPost -102452. logLik -97511.1 edf 241.87 eps 0.2153 iteration  26
AICc 195478.5 logPost -105979. logLik -97492.5 edf 233.97 eps 0.1975 iteration  27
AICc 195459.8 logPost -105821. logLik -97484.3 edf 232.87 eps 0.1229 iteration  28
AICc 195452.8 logPost -105786. logLik -97480.7 edf 233.00 eps 0.0596 iteration  29
AICc 195450.2 logPost -105760. logLik -97479.2 edf 233.12 eps 0.0244 iteration  30
AICc 195434.7 logPost -105734. logLik -97478.5 edf 226.82 eps 0.0150 iteration  31
AICc 195434.4 logPost -105670. logLik -97478.2 edf 226.95 eps 0.0105 iteration  32
AICc 195434.0 logPost -105656. logLik -97478.0 edf 226.91 eps 0.0067 iteration  33
AICc 195433.9 logPost -105661. logLik -97477.9 edf 226.96 eps 0.0072 iteration  34
AICc 195433.9 logPost -105663. logLik -97477.9 edf 226.98 eps 0.0020 iteration  35
AICc 195433.9 logPost -105663. logLik -97477.9 edf 226.99 eps 0.0010 iteration  36
AICc 195433.9 logPost -105664. logLik -97477.9 edf 226.99 eps 0.0008 iteration  37
AICc 195433.8 logPost -105664. logLik -97477.9 edf 226.99 eps 0.0004 iteration  38
AICc 195433.8 logPost -105664. logLik -97477.9 edf 226.99 eps 0.0002 iteration  39
AICc 195433.8 logPost -105664. logLik -97477.9 edf 226.99 eps 0.0002 iteration  40
AICc 195433.9 logPost -105670. logLik -97477.9 edf 227.00 eps 0.0001 iteration  41
AICc 195433.9 logPost -105670. logLik -97477.9 edf 227.00 eps 0.0001 iteration  42
AICc 195433.9 logPost -105670. logLik -97477.9 edf 227.00 eps 0.0001 iteration  42
elapsed time:  1.76min
Starting the sampler...

|                    |   0%  5.34min
|*                   |   5%  4.99min 15.77sec
|**                  |  10%  4.11min 27.39sec
|***                 |  15%  4.24min 44.85sec
|****                |  20%  4.24min  1.06min
|*****               |  25%  4.25min  1.42min
|******              |  30%  3.84min  1.65min
|*******             |  35%  3.58min  1.93min
|********            |  40%  3.34min  2.23min
|*********           |  45%  3.15min  2.58min
|**********          |  50%  2.93min  2.93min
|***********         |  55%  2.60min  3.18min
|************        |  60%  2.28min  3.43min
|*************       |  65%  2.03min  3.77min
|**************      |  70%  1.76min  4.11min
|***************     |  75%  1.46min  4.37min
|****************    |  80%  1.15min  4.59min
|*****************   |  85% 50.95sec  4.81min
|******************  |  90% 33.85sec  5.08min
|******************* |  95% 17.13sec  5.43min
|********************| 100%  0.00sec  5.70min

summary(multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo)

Call:
bamlss(formula = f_rice_wheat_yield_MRF_corr_endo_rev_non_struct_pointgeo, 
    family = mvnchol_bamlss(k = 2), data = Irrig_Rev_rice_wheat_sp, 
    type = "modified")
---
Family: mvnchol 
Link function: mu1 = identity, mu2 = identity, lamdiag1 = log, lamdiag2 = log, lambda12 = identity
*---
Formula mu1:
---
revenue_rice ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(Longitude, Latitude)
-
Parametric coefficients:
                          Mean  2.5%   50% 97.5% parameters
(Intercept)              48390 48283 48419 48425      48706
rice_duration_class_long  1696  1657  1657  2025       1540
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 4.558e-03 1.958e-27 8.076e-16     0
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     2.542e+08 1.715e+07 1.393e+08 1.319e+09
s(sowdate_fmt_rice_day).alpha     1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_rice_day).edf       4.708e+00 2.762e+00 4.663e+00 7.048e+00
s(g_q5305_irrig_times_rice).tau21 2.572e+08 2.561e+07 1.459e+08 1.174e+09
s(g_q5305_irrig_times_rice).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(g_q5305_irrig_times_rice).edf   5.621e+00 3.857e+00 5.583e+00 7.599e+00
s(nperha_rice).tau21              5.679e+06 8.042e+00 1.542e+04 5.595e+07
s(nperha_rice).alpha              1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(nperha_rice).edf                1.379e+00 9.539e-01 1.005e+00 3.614e+00
s(p2o5perha_rice).tau21           5.541e+06 1.433e+00 1.026e+03 6.142e+07
s(p2o5perha_rice).alpha           1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(p2o5perha_rice).edf             1.261e+00 7.974e-01 1.000e+00 3.684e+00
s(Longitude,Latitude).tau21       5.990e+08 3.297e+08 5.630e+08 1.074e+09
s(Longitude,Latitude).alpha       1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Longitude,Latitude).edf         2.614e+01 2.473e+01 2.616e+01 2.735e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21      8.397e+10
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf        2.401e+00
s(g_q5305_irrig_times_rice).tau21  8.526e+10
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf    1.403e+00
s(nperha_rice).tau21               7.576e+10
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                 2.287e+00
s(p2o5perha_rice).tau21            1.404e+10
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf              8.797e+00
s(Longitude,Latitude).tau21        2.059e+10
s(Longitude,Latitude).alpha               NA
s(Longitude,Latitude).edf          2.892e+01
---
Formula mu2:
---
revenue_wheat ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(Longitude, Latitude)
-
Parametric coefficients:
                        Mean     2.5%      50%    97.5% parameters
(Intercept)         19824.35 19519.95 19771.75 20515.01   22591.78
variety_type_NMWV    3822.32  3371.33  3739.70  4615.76    3391.73
g_q5305_irrig_times  5898.04  5652.76  5930.24  5994.93    5508.12
nperha                 17.77    11.99    15.01    25.08      12.16
p2o5perha              75.45    63.33    79.43    82.43      58.50
-
Acceptance probability:
           Mean      2.5%       50% 97.5%
alpha 8.818e-03 1.915e-26 5.928e-15 0.005
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 9.844e+06 6.101e+01 1.501e+05 8.248e+07
s(sowdate_fmt_wheat_day).alpha 1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(sowdate_fmt_wheat_day).edf   1.794e+00 9.971e-01 1.107e+00 4.811e+00
s(Longitude,Latitude).tau21    2.990e+08 1.425e+08 2.736e+08 5.825e+08
s(Longitude,Latitude).alpha    1.000e+00 1.000e+00 1.000e+00 1.000e+00
s(Longitude,Latitude).edf      2.589e+01 2.405e+01 2.592e+01 2.733e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21  9.950e+08
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf    7.392e+00
s(Longitude,Latitude).tau21     4.375e+08
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf       2.693e+01
---
Formula lamdiag1:
---
lamdiag1 ~ 1 + rice_duration_class_long + s(sowdate_fmt_rice_day) + 
    s(g_q5305_irrig_times_rice) + s(nperha_rice) + s(p2o5perha_rice) + 
    s(Longitude, Latitude)
-
Parametric coefficients:
                            Mean    2.5%     50%   97.5% parameters
(Intercept)              -9.4633 -9.4961 -9.4632 -9.4294     -9.447
rice_duration_class_long -0.1614 -0.2173 -0.1599 -0.1108     -0.154
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9789 0.8419 0.9995     1
-
Smooth terms:
                                       Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21     3.182e-02 9.862e-05 5.889e-03 2.598e-01
s(sowdate_fmt_rice_day).alpha     9.708e-01 7.566e-01 9.994e-01 1.000e+00
s(sowdate_fmt_rice_day).edf       1.711e+00 1.009e+00 1.412e+00 3.954e+00
s(g_q5305_irrig_times_rice).tau21 1.515e-01 7.080e-05 3.569e-03 1.523e+00
s(g_q5305_irrig_times_rice).alpha 9.532e-01 6.308e-01 9.986e-01 1.000e+00
s(g_q5305_irrig_times_rice).edf   2.529e+00 1.038e+00 1.862e+00 6.944e+00
s(nperha_rice).tau21              5.033e-01 8.451e-04 1.038e-01 3.973e+00
s(nperha_rice).alpha              8.899e-01 2.529e-01 9.902e-01 1.000e+00
s(nperha_rice).edf                3.531e+00 1.086e+00 3.275e+00 7.322e+00
s(p2o5perha_rice).tau21           1.754e+00 2.745e-03 9.278e-01 7.516e+00
s(p2o5perha_rice).alpha           7.364e-01 3.494e-03 9.240e-01 1.000e+00
s(p2o5perha_rice).edf             4.963e+00 1.266e+00 5.379e+00 7.404e+00
s(Longitude,Latitude).tau21       1.117e+00 5.414e-01 1.060e+00 2.100e+00
s(Longitude,Latitude).alpha       6.354e-01 6.446e-02 6.314e-01 1.000e+00
s(Longitude,Latitude).edf         2.511e+01 2.283e+01 2.521e+01 2.682e+01
                                  parameters
s(sowdate_fmt_rice_day).tau21          0.006
s(sowdate_fmt_rice_day).alpha             NA
s(sowdate_fmt_rice_day).edf            1.425
s(g_q5305_irrig_times_rice).tau21      0.722
s(g_q5305_irrig_times_rice).alpha         NA
s(g_q5305_irrig_times_rice).edf        6.164
s(nperha_rice).tau21                   8.456
s(nperha_rice).alpha                      NA
s(nperha_rice).edf                     7.813
s(p2o5perha_rice).tau21             1941.379
s(p2o5perha_rice).alpha                   NA
s(p2o5perha_rice).edf                  8.944
s(Longitude,Latitude).tau21            0.993
s(Longitude,Latitude).alpha               NA
s(Longitude,Latitude).edf             25.056
---
Formula lamdiag2:
---
lamdiag2 ~ 1 + variety_type_NMWV + s(sowdate_fmt_wheat_day) + 
    g_q5305_irrig_times + nperha + p2o5perha + s(Longitude, Latitude)
-
Parametric coefficients:
                          Mean       2.5%        50%      97.5% parameters
(Intercept)         -8.8421512 -8.9500230 -8.8438418 -8.7339565     -8.820
variety_type_NMWV   -0.1878189 -0.2361897 -0.1875278 -0.1363126     -0.194
g_q5305_irrig_times -0.1207840 -0.1517710 -0.1209172 -0.0890884     -0.127
nperha               0.0012399  0.0005045  0.0012535  0.0018686      0.001
p2o5perha           -0.0024816 -0.0036651 -0.0024982 -0.0013055     -0.003
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9425 0.6393 0.9931     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_wheat_day).tau21 1.897e-01 1.634e-04 8.161e-02 9.310e-01
s(sowdate_fmt_wheat_day).alpha 9.424e-01 5.772e-01 9.981e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   3.060e+00 1.021e+00 3.012e+00 5.391e+00
s(Longitude,Latitude).tau21    8.076e-01 3.918e-01 7.669e-01 1.488e+00
s(Longitude,Latitude).alpha    6.446e-01 8.818e-02 6.656e-01 1.000e+00
s(Longitude,Latitude).edf      2.423e+01 2.167e+01 2.434e+01 2.624e+01
                               parameters
s(sowdate_fmt_wheat_day).tau21      0.047
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf        2.602
s(Longitude,Latitude).tau21        41.379
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf          28.878
---
Formula lambda12:
---
lambda12 ~ 1 + g_q5305_irrig_times_rice + g_q5305_irrig_times + 
    nperha + p2o5perha + rice_duration_class_long + variety_type_NMWV + 
    s(sowdate_fmt_rice_day) + s(sowdate_fmt_wheat_day) + s(Longitude, 
    Latitude)
-
Parametric coefficients:
                               Mean       2.5%        50%      97.5% parameters
(Intercept)              -3.732e-06 -1.364e-05 -3.776e-06  6.860e-06          0
g_q5305_irrig_times_rice  6.735e-08 -9.469e-07  7.469e-08  9.686e-07          0
g_q5305_irrig_times      -1.360e-06 -4.223e-06 -1.328e-06  1.577e-06          0
nperha                   -4.994e-08 -1.124e-07 -4.897e-08  1.372e-08          0
p2o5perha                -5.504e-08 -1.763e-07 -5.573e-08  6.918e-08          0
rice_duration_class_long -5.151e-06 -1.016e-05 -5.027e-06 -7.769e-07          0
variety_type_NMWV         1.265e-06 -4.631e-06  1.273e-06  6.353e-06          0
-
Acceptance probability:
        Mean   2.5%    50% 97.5%
alpha 0.9337 0.6169 0.9898     1
-
Smooth terms:
                                    Mean      2.5%       50%     97.5%
s(sowdate_fmt_rice_day).tau21  3.298e-05 1.114e-05 2.714e-05 8.419e-05
s(sowdate_fmt_rice_day).alpha  9.746e-01 8.347e-01 9.983e-01 1.000e+00
s(sowdate_fmt_rice_day).edf    8.989e+00 8.975e+00 8.990e+00 8.997e+00
s(sowdate_fmt_wheat_day).tau21 3.431e-05 1.159e-05 2.756e-05 9.216e-05
s(sowdate_fmt_wheat_day).alpha 9.653e-01 7.931e-01 9.993e-01 1.000e+00
s(sowdate_fmt_wheat_day).edf   8.991e+00 8.980e+00 8.992e+00 8.998e+00
s(Longitude,Latitude).tau21    7.996e-06 4.830e-06 7.665e-06 1.342e-05
s(Longitude,Latitude).alpha    7.134e-01 2.512e-02 8.682e-01 1.000e+00
s(Longitude,Latitude).edf      2.899e+01 2.899e+01 2.899e+01 2.900e+01
                               parameters
s(sowdate_fmt_rice_day).tau21   369816541
s(sowdate_fmt_rice_day).alpha          NA
s(sowdate_fmt_rice_day).edf             9
s(sowdate_fmt_wheat_day).tau21   77206761
s(sowdate_fmt_wheat_day).alpha         NA
s(sowdate_fmt_wheat_day).edf            9
s(Longitude,Latitude).tau21       4230447
s(Longitude,Latitude).alpha            NA
s(Longitude,Latitude).edf              29
---
Sampler summary:
-
DIC = 195483 logLik = -97641.41 pd = 200.1402
runtime = 343.5
---
Optimizer summary:
-
AICc = 195433.9 edf = 227.0086 logLik = -97477.91
logPost = -105670.8 nobs = 4527 runtime = 105.72

dev.off()

null device 
          1 

plot(multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo)
dev.off()

null device 
          1 

multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo_fitted=multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo$fitted.values

multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo_fitted=as.data.frame(multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo_fitted)

Irrig_Rev_rice_wheat_sp$revenue_non_struct_lambda12 <- predict(multivariate_geo_sow_MRF_corr_endo_rev_non_struct_pointgeo,model = "lambda12")

library(tmap)
tmap_mode("plot")
tm_shape(Irrig_Rev_rice_wheat_sp) +
  tm_dots(col = "revenue_non_struct_lambda12", title = "Rice-wheat revenue equation \n correlation parameter", 
          style = "quantile",palette = "-Spectral",
          size = 0.5) +
  tm_layout(legend.outside = TRUE)+
  tm_legend(text.size = 1)  


# Compare the models using DIC

#DIC(multivariate_geo_sow_MRF_corr_endo,multivariate_geo_sow_MRF_corr_endo_more)

# library(distreg.vis)
# library(bamlss)
# 
# library(mvnchol)
# if (interactive()) {
#   distreg.vis:: vis()
# }

8 Conclusion